I don't think there's anything preventing the current roles from being made into more narrative concepts. For example:
Guardian - Defender
Ravager - Striker
General - Leader
Tactician - Controller
Those are just different names for the same thing and do not address the issue.
Role is inherently tied to what a class does, and what your class does tends to be tied into your concept (a 4e Rogue who isn't interested in putting the hurt on enemies is a pretty poor Rogue).
In 1E, a Thief was there to handle the traps. Combat was a side issue for the thief, although he could manage it. But backstab was a bit rare, not an every round thing.
The game has morphed such that every single class has to be good at combat. Recent 5E discussions are that every single class has to be good at non-combat.
All of this is in the opposite direction of narrative direction. A player cannot really play a bumbling innkeeper who just happens to go on adventures and hang in the back, using his mechanical skills to get past traps. He must also be a good fighter of some type and a good negotiator of some type.
Or the archaeology professor who goes spelunking with the adventurers, but wouldn't know one side of a sword from another. But, he knows his ancient languages and what the weird objects are.
The Bard who has no Str and has no Dex can wield his sword just as good as or even better than the high Str high Dex Fighter.
Narrative has gotten lost in the world of balanced and equal mechanics, and the discussions of segregating powers into role, class, and power source are doing that even more.
My take is in order for 5E to go back to the 1E roots (without Vancian magic and the power issues it created) is for the game to start with ability scores, not with classes, roles, and power sources.
Martial powers should be Str/Dex based. Weapon attacks should all be martial powers. If a PC doesn't have a secondary role (multi-class or some how), then s/he can only do melee basic and ranged basic attacks. S/he isn't trained in the martial power source enough to do advanced martial abilities.
Magic should become MAGIC again.
This is very important, so I'd like to reiterate it.
Magic should become
MAGIC again.
The Martial power source shouldn't have taunts like a video game and should never target Will defense. Fighters and Rogues should be able to do amazing things like shift across the battlefield quickly or super climb a wall, but they shouldn't be able to Fly or go Invisible or Teleport or Heal. Just like Wizards shouldn't be able to wield a sword to do anything at all (other than a melee basic attack) unless they multi-class into a martial power source class.
Magic should be Int/Wis/Cha/Con based. Magic can be Arcane, Divine, Primal, or Psionic (granted, Divine and Primal could be subcategories of a Spiritual power source, but they do make sense apart). 5E should avoid the concept of 50 flavors of ice cream when discussing power sources. Let the bad guys have the Shadow power source and the Elemental power source and the 100 other ways people can think of to create new ones.
Arcane is Int/Wis.
Divine is Wis/Cha.
Martial is Str/Dex.
Primal is Con/Wis.
Psionic is Int/Cha.
There are literally thousands of options with martial, arcane, primal, divine, and psionic.
There should be no Assassin class per se. An Assassin is a Rogue who might dip his toe into the Arcane power source a bit and/or dip his toe into mundane poisons (an alchemist skill, not a power source).
Divine should be active gods.
Primal should be ancient gods/spirits/demons/devils/primordials (primordials, primal, anyone see a connection?).
A Warlock should be as much Primal as Arcane. He doesn't just deal with magic, he also deals with ancient and mysterious beings. That's something that is mostly hand waved away in 4E. Warlock powers themselves should have consequences of use, just like Druid powers should interact with spirits and have consequences of use.
Each class should have it's own role(s) and power sources that make that class unique. Classes that have two power sources are the true hybrid PCs. There is no such thing as a hybrid class because that's what some classes are.
Cleric Divine
Fighter Martial
Druid Primal
Rogue Martial
Sorcerer Arcane
Wizard Arcane
Barbarian Martial|Primal
Bard Martial|Arcane
Monk Martial|Psionic
Paladin Martial|Divine
Ranger Martial|Primal
Warlock Arcane|Primal
Note: I dropped roles here for these classes. More on that later.
Based on which powers a player takes determines what roles that PC has.
The concept here is that some classes are single power source and some classes are dual power source.
The designers should limit what each power source can do. The concept that everyone can heal is too video gamey. The Arcane and Martial power sources should not be able to heal. Period.
The Psionic power source can heal, but only self heal.
Healing is the purview of the Divine power source and the Primal power source. Healing should be healing again. Combat is dangerous and actually does damage PCs. There should be no combat chearleaders. The ability to dig deep should occur once per encounter and be called Second Wind. A Martial power source PC might be able to encourage another PC to dig deep, but that is really having the other PC use his Second Wind.
The Divine power source cannot Teleport, etc.
Take the main capabilities of the game and segregate them based on power source.
Every power source can do damage.
I can definitely see the Primal power source as being relatively benign as long as the PC is doing minor effects. But, major effects might have a personal cost. The modern gods of the Divine power source have power to spare. The ancient gods and spirits have limited power. So, when the PC throws out a powerful effect, the PC also has something detrimental happen. This can be balanced out by the powerful effects being stronger or more versatile or last longer via in game mechanics than the Divine powers.
By segregating the game like this, the power sources become more than a way to just split up classes. They becomes ways to really narratively define the classes.
Martial classes are martial. They use weapons. They don't use magic. Magic is now special again, but each type of magic (arcane, divine, primal, and psionic) is unique and has it's own very strong game mechanics and narrative flavor.
Arcane casters are a hodge podge of magic. They can go Invisible, but not as well as Primal casters can (who can fight for short periods of time while invisible). Arcane casters can use Telepathy, but nowhere near as well as Psionic casters. They can create a Wall of Fire or a Wall of Fog, but nowhere near as good as a Primal casters.
Psionic PCs have limits as to what they can affect outside their bodies (telepathy, telekinesis, etc.), but they can do amazing things with their own bodies (boost mental defenses, heal, boost their physical strength, etc.). But, they cannot create Walls of Fire. Elemental powers are the purview of the Arcane and Primal power sources. Even divine PCs have no elemental powers.
Each power source should have it's own strengths and weaknesses and even things that it cannot do at all.
Instead of discussing roles, I think it is more important to get back to the narrative roots and discuss power sources.
Roles can even be dropped completely. They make little narrative sense.
Instead, a Wizard can take a striker like single target Lightning power. When using it, he's a striker.
A Fighter can take a Control power where he targets enemies in a one square area and he knocks them all prone. Or, he takes a Leader power to distract an enemy such that they are debuffed fighting other PCs.
The powers themselves dictate what the role of the PC is that round, not the class of the PC.
Then, we do not need roles.
Class roles are artificial. Get rid of them. Bye bye.
Power roles make sense. At the moment, my Rogue is being a striker by damaging a foe. At the moment, my Rogue is being a controller by blinding a foe.
By shifting the roles to the powers, the player decides which powers to take and hence, which roles his PC typically does.
And the power sources dictate the utility of any given power. For example, if the game designers determine that the Primal power source deals with elemental powers stronger than the Arcane power source does, it means that at the same level that the Arcane caster fires Lightning against a single foe, the Primal caster fires Lightning against an area. At the same level the Arcane caster fires Lightning against an area, the Primal caster fires Lightning against enemies only in an area.
Game design segregates capabilities not only into each power source, but how useful/powerful those capabilities (Tier 1 is strong/useful, Tier 2 is somewhat capable, Tier 3 is barely able to do it, and Tier 4 is not able to do it).
Primal is Tier 1 for elemental powers, but Tier 3 for teleport powers.
Arcane is Tier 2 for elemental powers, but Tier 1 for teleport powers.
Divine is Tier 1 for healing powers, Primal is Tier 2, Psionic is Tier 3, and Arcane/Martial are Tier 4.
The game is balanced by power source for what that power source can and cannot do and how well it can do it. The tiers are game design mechanics. The players do not see those, only the game designers do. But, the players can infer them. The Martial class does not heal, so it is Tier 4 in healing.
And then, multiclassing can come into play so that PCs can acquire minor capabilities outside of their power source(s). You want a Wizard who can heal Daily? Sure. Use up the appropriate resources and he can heal. You want a Wizard who can heal once per Encounter? Sure. Use up a lot more resources and he can heal that often.
Once the game capabilities are segregated by power source, powers can then be further segregated by class.
A Paladin can do a Holy Smite which does physical and radiant damage, but if a Cleric does not have a multi-class martial power source, s/he cannot do Holy Smite.
On the other hand, both Clerics and Paladins can Turn Undead. Since Clerics are single power source and Paladins are dual power source, Clerics turn undead better than Paladins do.
Paladins use melee weapons better than Clerics do, but not as well as Fighters or Rogues do.
Game balance. Pros and Cons. Not everyone can do everything shy of multi-class delving into other power sources and even then, they cannot do it as well as PCs who live and breathe that power source.