5e, in my view, fixed (or tried to) the 3e caster problem the wrong way: they nerfed (or removed) a lot of spells while still leaving them too easy to cast. Better to have made them harder to cast (do away completely with combat casting as a concept*, make spells easy to interrupt, etc.) but leave some power in 'em. I don't at all mind a wizard being able to unleash lots of damage now and then.I think you over-estimate a caster's versatility. A 5e cleric does have about 15 spells to choose from at a given level (not much more than your dozen). Wizards only get a guarantee of knowing two spells for every level they gain. Furthermore, a fighter probably IS the highest-damage-output at most levels. Compare a wizard who fire bolts (1d10) to a fighter who longbows (1d8+DEX bonus), or even better a fighter who Mauls (2d6+STR bonus).
Of these I far prefer the battlemaster option, where it leads and inspires from the front by showing the party how it's done. With risk comes reward.In fact, part of the reason a battlemaster is in some ways a sub-par warlord is that the battlemaster still makes a lot of attacks themselves, and gets their power from that, while warlord fans seem to want a class who gets a lot of their damage potential from giving extra actions to their allies. The battlemaster gives actions to allies as a cherry on top of being an engine of destruction themselves, rather than giving actions to allies as a base part of how they contribute to damage/defense.
Yes, but that's not sufficient description of the sweetmeat. I've watched several arguments between warlord proponents over what is an acceptable warlord, largely based on what "non-magical, non-supernatural" really means.
For example, there's, "Not magical or supernatural, in that things like anti-magic shell or dispel magic don't effect it, but really I'm okay with them being pretty spectacular and unexplainable". Then there's, "not magical or supernatural, in that it is limited to effects that I personally imagine happening in my own *mundane* real world".
Heh. That's why the fighter in out dragonlance game has the lowest damage output. By a long ways.
Compare a Sorcerer who Fire Bolts for 2d10 every shot. That's more than your maul wielding fighter. And that's the least damaging attack he makes.
I am sure anyone who cringes every time they hear the word Warlord (as well as Warlord fans who don't like refluffing) might not like this but how about presenting a 5e Warlord as a magical class but with absolutely minimal fluff other than something like "using a lost mythic war magic from a previous epoch," "blessed by the gods of war" or "a chosen one manifesting the spirit of war itself." *snip* Any thoughts? Any objections?
If you want to be fair, compare that 2d10 fire bolt to a fighter who is using Extra Attack, which is what they'd get at the same level - a 2d10 fire bolt vs. a 2x(1d8+DEX) for a long bow or a 2x(2d6+STR) for a melee attack. It's pretty obvious which one is better.
If you want to start taking daily spells into consideration, we also need to look at Action Surge. Your flagship damage spell for a 5th level sorcerer is Fireball, which deals roughly 112 damage (8d6 * 4 using the DMG's rules for estimating the number of targets in an area effect and presuming all fail their saves). Compare with Mr. Maul (lets presume a +3 STR bonus, not crazy optimized, and just like the sorc's victims all fail, Mr. Maul always hits), and we see ~ 40 damage every time a fighter action surges, and we can presume about 3 action surges per day, which gives us 120 in the same interval.
I'm hardly doing rocket surgery on this, and there's corner things to take into account (your DL character is a defensive fighter, and the damaging sorcerer is a damage-focused sorcerer), but it is not clear on the face of it that a fighter is any less capable of damage than a mage of equivalent level.
Which brings us back to the idea that in 2e, a fighter was pretty much the undisputed lord of damage for the first 5 levels or so. A lot of people found that inadequate (especially by 6th level!). In fact, the Complete Fighter's Handbook even gets all defensive about it on its back cover: "Who says fighters are the poor cousins of the AD&D game?"
Fighters being inadequate is a narrative with a lot of history behind it, history as old as the D&D game itself. In 5e, it does not seem to be a true narrative in practice, speaking from my experience.
I think you over-estimate a caster's versatility. A 5e cleric does have about 15 spells to choose from at a given level (not much more than your dozen). Wizards only get a guarantee of knowing two spells for every level they gain. Furthermore, a fighter probably IS the highest-damage-output at most levels. Compare a wizard who fire bolts (1d10) to a fighter who longbows (1d8+DEX bonus), or even better a fighter who Mauls (2d6+STR bonus).
In fact, part of the reason a battlemaster is in some ways a sub-par warlord is that the battlemaster still makes a lot of attacks themselves, and gets their power from that, while warlord fans seem to want a class who gets a lot of their damage potential from giving extra actions to their allies. The battlemaster gives actions to allies as a cherry on top of being an engine of destruction themselves, rather than giving actions to allies as a base part of how they contribute to damage/defense.
A well played fighter is durable and damaging. The paladin may lay down some damage when spending his spells in melee, especially on a crit, but if the fighter actually thinks about using his bow, he should be easily able to hold up to the expectations.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.