In short, the solutions that 1e presents to the problems it inadvertently also helped create are antiquated to more contemporaneous game design mores. Uneven leveling between classes, for example, would be regarded as anathematic given its persistent absence in 3-5e or the common use of milestone leveling. Or likewise the "super weak now for super strong later" model for wizards also does not hold much water given current playmodes that rarely exceed 8th level. So though you may naturally disagree given your own valid play preferences, I do not think that looking to 1e is necessarily the best way to go about addressing these issues for the current gaming Zeitgeist.
And those weren't even the 1e-based solutions I was thinking of!
I was thinking more along the lines of making casting very interruptable (even being attacked while casting in 1e wrecked the spell, whether the attacker rolled well enough to hit you or not; and taking damage from any source while casting would also wreck a spell) and making it take longer - i.e. reintroducing the idea of casting times - to provide in effect a window of interruption. Do away with and completely ban anything even remotely resembling 'combat casting'. Force casters to roll to aim their spells if cast under pressure or in combat (not RAW 1e; this one's a houserule we brought in decades ago). Bring back bouncing lightning and expanding fireball to make these spells dangerous again. Put wizard-types back to a d4 to make 'em squishier, and if low-level survival is too much of a problem then give 'em two dice at 1st level like 1e Rangers used to have.
By the way, rarely exceeding 8th level isn't new.

(though I thought the general upper limit was more like 12th-ish, as that's about where a lot of AP's end you up)
As for possible solutions? I hesitate to say. Numerous possible solutions exist, especially given how other systems tackle the problem, but whether those solutions would be palpable for D&D's fanbase is another matter entirely.
As 4e and the reception of D&D attests, people gleefully accept power expansions for wizards but are reluctant to give them up. 5e did manage to do so, but it benefited from being perceived as a return to normal from 4e, even as it curtailed the excesses of 3e.
Yeah, 3e let a lot of cats out of bags it shouldn't have.
But I also don't think that 4e's proposed solutions to the problem should be dismissed so easily merely for being part of 4e. Especially given how some of these issues that plagued the reception of 4e were a matter of packaging and presentation rather than content. Furthermore, while tradition is one of D&D's greatest strengths, it also makes it incredibly intractable to change. This is especially true for the spells, spell tiers, and such that have become iconic for wizards and the like. Could you imagine D&D if spellcasting only went to fifth level spells? Or a considerably smaller available spell list?
Actually, I kinda could imagine that. It would take some serious tweakage to avoid casters running out of new stuff at level-up around 10th level, but it could be done.
But from all I can tell 4e sort of went the other way, making all the other classes work - or be able to work - like casters.
And regarding fighters? My own experience has sadly taught me that people are remarkably hesitant to let fighters have cool and fantastic things. Epic wizards can rewrite the cosmos, but epic fighters are rarely afforded their own mythic class fantasies.
There's a reason for that: fighters - and thieves/rogues, to some extent - are seen as being much more grounded in reality. People want to be able to relate to these classes in a much more straightforward way than they do (or can) to clerics and wizards, who are demonstrably different from our known reality.
I've played lots of both, and I relate to - and play, and want to play - my fighter types and caster types in quite different ways. For the fighters I don't want any complications - no powers, no feats, no nuthin'. Just give me a weapon, give me an opponent, and let me hit it till it falls down...oh, and pass me a beer, will ya? I relate to these guys as people I could go down to the local bar and meet...if the local bar got time-phased back to year 1500.
But for the wizards and clerics I accept the complication inherent in having to manage a spell list and at least vaguely know what these spells can do. I relate to them as people when they're not casting, but when they're casting that relationship drifts into gamist mode pretty quickly. The one complication I really despise is pre-memorization of spells; in my own game I've got rid of it.
Unserious Brainstorming: One could potentially scale back spells. Beyond the Wall makes spell slots equal to Mage level, going to level 10. Every spell cast costs one slot. (It also uses cantrips and rituals.) If one wanted to preserve spell levels in D&D, one could then propose that a similar system in D&D could have a 2nd level spell cost two slots, a 3rd level spell cost three slots, and so on. You could even choose to scale spells to raise the power level. This seems like a mix of spell lots and a mana pool system. Adjust a possible max number of spell slots for what you find most appropriate. So if you followed the BtW model of spells caster per day equals to class level, then a presumably level 20 character could cast two level 9 spells per day, but not have too much afterwards. But you could then provide the wizard with more sagely in-game utility and such that is not purely magical. Though D&D likes having the wizard as a magical badass, it does not really capture the sage well apart from "you have the appropriate Arcana skill."
The first way to scale back spells is to do away with non-slot cantrips or at-wills. The second is to put ritual and slot casting into the same system - a spell's a spell no matter how you cast it. The third is to make spells a bit more risky in some cases (see above); or maybe more costly, but that's annoying. The fourth is to look at how some spells got broken particularly by 3e (polymorph, anyone?) and fix them; and here 1e can give some decent guidance. A fifth would be to knock off some spells that trample on the niches of other classes (Knock, Find Traps, Spider Climb - or whatever their current equivalents are) and don't replace them. A sixth would be to make a bunch of spells currently with range of touch have range of self instead - Fly, Silence, Polymorph just to name a few - to rein them in. A seventh way would be to do away with metamagic feats. An eighth would be to do away with slot flexibility - if you're out of 1st level slots but you have some 2nd-level slots left then sorry, you're stuck with casting 2nd-level spells until tomorrow morning; your 1st-level spells are unavailable because you ran 'em out.
The thing I'd give them in return, were it me in charge of all this, is that spell pre-memorization would disappear never to return. All casters would work like 3e Sorcerers - if you have the spell in your book (or on your list, if a cleric) and you have a slot to cast it with then you can cast it. Period. Full wild-card by level. (I do it this way, and the pleasant side-effect has been that I see spells get cast that otherwise would never see the light of day)
As for the sage idea, the problem with a PC knowing so much is it means there's that much less for that PC (and by extension, player) to learn and discover. That said, if you're running a canned setting and one of your players happens to be well-versed in said setting I could see a place for this.
Lan-"sometimes the most dangerous thing a 1e party has to face is the friendly fire from their own casters"-efan