"My Level X character is equal to your Level X character." Even substituting the more accurate gauge of "X experience points", that's not really a big deal in old D&D. After all, the basic idea is that you should rack up more XP in the first place via skilled play than does some blunderer. And you're not forced to give up your levels just because a total newbie gets to experience starting from 1st (although you're probably not taking a Lord or Wizard on the same expedition!).
Viable. You conflate two different "level" balance ideas. The first is that a 12th level thief and a 12th level magic-user should has some nod to balance (options available, raw power, or spotlight time) and the second is that a 12th level thief should be equal to a 1st level fighter (who is replacing the 12th level magic-user who just died).
The second is preposterous as it defeats the point of levels. No one, except a few interested in redesigning a game from scratch, feels 1st and 12th level should roughly the same power level.
The first is IMHO vital. Otherwise you create a "tier" system where some classes begin (or end) simply better than others. If it was a simple as "fighters start good, but get worse while mages just the opposite) it'd be passable, but both classes can overshadow thieves, while a ranger is clearly a superior choice to a fighter, and a well-run cleric can overshadow both.
"My character is just as good as your character in combat." Nope. Magic-users and thieves are not fighters.
Combat is a ubiquitous marker to use. I still prefer the concept of "each character excels in a niche no other class can match". Balance. Fighters should dominate combat. Thieves should be the perfect scout/spy/assassin. Clerics are masters of healing/defensive magic, mages should have offensive, summoning and transportation magic bar-none. Other classes can dabble in a second role (clerics make fine 2nd fighters, mages get some defensive spells) but no class should do its role AND another role better than the class designed for it. (IE a ranger is a better scout/spy and combatant than a fighter AND thief).
Lastly, every class should have some option in combat, even if its less-superior than the fighters. Thieves get backstab, clerics are decent fighters with a bit of offense, mages have polymorphs and summons, etc. NOTHING is more boring than sitting through combat after combat doing nothing (or maybe a few points of missile damage) while your friends are having a blast hacking up goblins or throwing fire-and-lightning.
"A or B or C is true of The Party." The Party, as a constant entity, was not part of the design. Conan and the Grey Mouser might team up to rob the Tower of Eels one session, then part ways. Conan might then accompany Thongor, Elric, and Tyana and some of her pirates for a raid. Then, Thongor, Tyana and Mouser (with a shipload of Mingols) might join Fafhrd on Rime Isle.
"A good party balance would be something like 40% fighters, 30% magic-users, 20% clerics and 10% thieves." - Lawrence Schick,
White Plume Mountain.
"The optimum mix for a group is 9 characters of various classes..." Gary Gygax,
Steading of the Hill Giant Chief.
D&D has ALWAYS been about the party. Its not a collection of individuals, its a TEAMWORK-based game. A good game should challenge all players and all classes that are there; the hallmark of a poor DM is one who believes all challenges should be overcome by only magic or combat alone.
"Each encounter should be 'level appropriate'" Not on the horizon. The players' estimation of risk and reward is key to the game.
Every encounter should be in a survivable range. If there is a dragon, even a powerful one the PCs have no business fighting, it should still be young enough the PCs might survive a breath-weapon strike while fleeing. Pitching a great wyrm with a blast so powerful its "save 1/2" damage is guaranteed to drop even the barbarian to -10 isn't a challenge, its a turkey shoot. If the PCs are foolish enough to want the fight the dragon, all bets are off. But having a fighting chance (even if its just to retreat) goes a long way to fostering good PC/DM will, and I find if PCs believe they will die from EVERYTHING (goblin ambushes at night, every lock a death-poisoned needle, every dragon a great wyrm) the game either slows down to the point of 45 minute argument at every door, or a group of WTF PCs kicking in every door in a moment of chaotic frenzy that would make a Toon Player proud.