I only just found this, and am quite excited. I've been pondering classes extensively in my own homebrews over the last year, so please excuse me for a little bit for being long-winded, giving my own 20 cents on the subject.
What does being a class mean? Thematically, it says something about what the character is, what they do, and what they can do. Mechanically, for vanilla D&D, as a reference, it amounts to the following:
HP at level 1
Skill points at level 1
Save bonuses at level 1
Class Skills list
Weapon and Armor proficiencies
Base attack bonus progression
Now, IMO, the multiclassing system in 3rd ed has 2 real faults. Giving out too much to starting level nonspellcasters, and too little to starting level spellcasters. The difficulty is presenting a level 1 character with enough to feel fully a part of its class, without making it superior to play a Ftr1/Bbn1/Rgr1/Rog1 over a standard 4th level character. (I've seen it done.) Add another, lesser fault of being unable to play a multiclass character concept at 1st level.
I'll get back to that in a sec. d20 Modern has all of those mechanical qualities of your base class, with a fraction of the thematic elements. Instead, your Occupation told you more about what your character is and does than your class. It really didn't fill the role of what your actual Occupation was often in practice, in my experience anyway, instead mostly being a "what I did before my life was hijacked by this adventuring" thing, or sometimes a "what I do as a day job to finance these crazy expeditions" thing.
So, here's what I propose: take all the "at first level" stuff out of classes, and wrap it into Backgrounds. (especially since I hate characters with absolutely no history or background at all, and having more specific background options than "I'm a cleric of pelor" ought to help there.) So a background would contain starting HP, starting saves, class skills, starting skill points, starting wealth/gear, starting proficiencies, perhaps an exclusive background talent, or whatever permutation of these things stays relevant to character creation in e20.
Given that, what would class mean? What's left? Well, now that who you are and were is no longer revolving around that decision, gaining a level in a class would mean how you grew and what you learned since your last level. Ie, the distribution of many hit points, new skill points, saves, talents, spells, and whatever you acquired.
For example, relative to the average as a baseline, a level in fighter would mean something like +2 hp, +0.16 fort, +0.25 base attack, 1 fighter talent, -2 skill points.
That breaks down into 2 parts: making you a more effective tank by trading some skill for some durability, and gaining iconic powers.
Assuming you want heavy multiclassing to be possible, and even encouraged if you're looking at very generic classes such that you expect most people to mix them to get their character concepts, like in Modern... what's the point of having 6 classes? What makes them sufficiently distinct in what they offer to be meaningfully different?
I'm asking a lot of rhetorical questions to try to elucidate my point, excuse me. I can't manage to be more direct and concise at 3am. Anyway; where I'm going with this, is that in effect, classes as you've been suggesting are mostly just arbitrary silos for talents. If a character can take no more than 1 talent per level, tracking your level in a given class is really just tracking your progress along the tree of one silo over another. The remainder is choosing where you want to be on the trade-off between durability, skills, and specials.
So ultimately, while this might be counterproductive to this conversation, I feel that the way to go is towards a point of classes=talent trees. Not a class contains talent trees, but a class is a talent tree. Wrap the small mechanical increases into progression along given talent trees, like +2 hp whenever you take a Dreadnought talent, or the like. This also preserves uniqueness and interestingness of your classes, without needing a bunch of totally generic classes struggled to name ungenerically. Any character could take a talent they meet the prereqs for from any tree; it would just be normal multiclassing. Classes wouldn't need to all be the same length, and it allows easy, natural progression into advanced/prestige classes as just talents with steeper pre-reqs. It also might make balancing classes against each other easier; you just balance each talent individually with pre-reqs vs benefits against other talents.
I understand that this might be taking things a little too far off the beaten path, but I figure, if anything, that's what e20 is for, so hopefully this will at least be food for thought.