Sorry, but are you kidding? Almost every non-leader class has at least one:
Assassin: Claim the Dead
Avenger: Renewing Strike
Barbarian: Life Thane Rage
Battlemind: Aspect of Elevated Harmony
Druid: Form of the Primeval Boar (pre-Essentials turning Druids into Leaders)
Fighter: Comeback Strike
Invoker: Death's Denial
Monk: Internal Power
Paladin: Paladins Judgment
Ranger: Wounded Beast
Sorcerer: Moon and the Stars
Swordmage: Rejuvenating Strike
Warden: Bear's Endurance
Warlock: Red Leeches of Nihal (I put this down as an example because it's temporary hit points which amount to the same thing, warlocks actually have several other actual healing powers)
Granted, many such powers are Dailies, but not all of them. And some of these classes have a dozen or more such powers.
All of which are MUCH more limited than any kind of healing your leader will provide. Look at Red Leeches of Nihal since you seem to like it... The power requires a standard action and occupies a daily slot to provide a bare HS worth of personal healing. The temp nature of the healing aside, it is a terrible power. Fighters have some similar powers, one of which actually allows to heal another PC, but again this is a bare HS worth of healing and requires a standard action. It is to put it bluntly a basically worthless power.
Now, if you are talking healing powers that heal others, then yeah, that might be 10% of the 150 to 200 or so non-leader healing powers in the game. But, a lot of them still exist. Remember, a PC only has to have one of them in order to heal.
Except pretty much invariably they require standard actions, take up slots better used for other things, etc. You're not going to get anything but the very most basic healing without being a leader and frankly it is almost never actually worth using 95% of these powers.
But compared to previous editions of the game, 4E is probably the most egregious about letting non-healers heal. There is a lot more role bleed over.
It is really not roll bleed over at all. Any 4e PC has Second Wind already. Most of the powers you can use which provide some form of healing are considerably WORSE than Second Wind. I hardly think this is stepping on the toes of the leader.
And the reason it happens in 4E is because everyone has powers. Everyone is a superhero. In previous editions, not everyone had spells.
And yet all the literature, myth, and other types of fiction from which D&D principally draws is rife with 'martial' heroes doing exactly these things. I find it to be entirely appropriate and 4e is vastly better at portraying these things than other editions have been (in 3.x there were options, but the costs were high or they required rather elaborate class poaching etc). I'm sorry, but your notion of some kind of divide between different types of 'magical' and 'non-magical' heroes simply doesn't hold up against the source material, nor do most players IME wish to be permanently consigned to "I hit it harder" just because they want to use a sword.
I'm after things like Artifacts or (expensive) Rituals that restore Healing Surges and/or possibly Daily powers (possibly with penalties associated with them such as cannot regain healing surges for a week or some such). The game allows someone to be brought back from the dead, but has no mechanisms for getting past 4 encounters per day. Huh?
I'm looking for MMMAAAGGGIIICCC!!!
BOOM, not wimper.
First of all, there's no hard and fast limitation of 4 encounters per day. This is entirely within the control of the DM. You want more encounters? Make them a bit weaker. You want restoration of daily resources, there are all kinds of options. DMG2 most certainly talks about possibilities like a 'fountain of healing' or whatnot. Artifacts are a totally blank slate, you can do ANYTHING with them. Make one up! What is WRONG with people these days that they can't simply drop what they want into their game? These things aren't covered in the PLAYER CHARACTER rules because they are simply not things that the players are supposed to be building around. They CAN get them, but that acquisition is strictly in the purview of the DM, where it really should be.
Honestly, where in AD&D were these kinds of things? I haven't read much of 3.x stuff, so I won't comment on that, but this kind of thing was ENTIRELY a DM resource in AD&D. I don't understand what you're complaining about. BOOM is "here's the DM's responsibility", so STEP UP!!!!
The Fountain of Youth
In Indiana Jones and the Last Crusade, drinking from the Holy Grail
In "The Lion, The Witch, and The Wardrobe" (1950), Father Christmas gave Lucy a cordial
In "The Slithering Shadow" (Conan, 1933), there was a golden wine that restored vigor and repaired wounds, bringing Conan back from the brink of death to full health.
Granted, they aren't "drinking healing potions in the middle of combat", but then again, that doesn't happen too often in 4E either.
Exactly, it doesn't happen often in 4e BY DESIGN because they actually looked at the rules and the sources for the game and said "gosh, this doesn't fit in well with the genre" and reduced its importance in the game.
The issue with "the hero's own resolve" is that it's overplayed here. It's allowed to be "every single encounter" or in the case of Warlords (and even Bards), it is every single encounter.
Until the PC exhausts his reserves, yes. Honestly, go back to the source material again. It is REPLETE with heroes getting back up and going on with nothing but grit. Heck, REAL LIFE is replete with these kinds of stories. Sorry, I don't even consider this kind of thing terribly unrealistic within the basic context of the game and its abstractions. It certainly fits in quite well with the action adventure genre.
It's the concept that wounds don't exist. We fight and fight, but we don't get wounded. We just get tired and then overcome being tired with personal resolve and cheerleader cheering up. Woo hoo! That concept is really over used in 4E and is not what I consider magical fantasy.
Except of course that hit points are abstract, so that is a rather dubious interpretation to start with. Secondly I see wounded heroes going on with nary a wince all over the place. Bruce Willis and Jackie Chan run around with bandages in practically every movie either of them ever made. Slap a bandage on it when you get a chance and off you go, good as new.
The one thing about 4E that I hope that they restore with 5E is the magic.
In 4E, most every PC has superpowers. Most every PC can heal. Most every PC has supernatural or magical ways to shrug off or avoid damage.
Every PC is a Jedi (i.e. with respect to displaying supernatural abilities).
It's not a matter of balancing the powers. It's a matter of segregating them.
One of the few things I like about Essentials is that some of the PCs now have most abilities that merely increase the umph of a melee basic attack without delving into supernatural effects.
Don't get me wrong. I enjoy playing 4E. I just find the roles and classes to be very overlapping, partially because most powers have supernatural or magical riders or effects. We can't just hit for damage, we have to also move foes or add bonuses and penalties to future rolls or yadda yadda yadda with almost every single power. There is also a ton of bookkeeping associated with all of these effects from most every single power / class feature / item / feat.
Syndrome (to Mr. Incredible): "And when I'm old and I've had my fun, I'll sell my inventions so that everyone can be superheroes. Everyone can be super. And when everyone's super, no one will be."
This is how I view 4E's magic. Everyone has it. Nearly every single monster (except minions for the most part). Every single PC. And they all have it in spades.
Yeah, we'll never agree. The last thing on earth I want to see is the return to the days where if you picked up a sword you were instantly turned into a second-rate lackey. 4e is far more true to its source material and fantasy tradition IMHO than any previous edition. I think they did a rather brilliant job of this actually. It is a magical fantasy world, magic is part of everything, and the personal 'magic' of the bad-assed sword wielding warrior is a welcome and LONG overdue addition to the game.
All I can really say is some 5e retro game where we have to go back to the old days because hey Gygax didn't do it the 4e way is NOT something I'd touch with a 10' pole.
I'd be OK with some way of organizing the rules so that there ARE a set of plausible mundane mechanics that can provide a core set that you can access easily. Forcing players to be limited to nothing but that simply because they picked the 'wrong' character concept is completely uninteresting to me.