I'm just making discussion here, but what would you think of a Shadow of the Demon Lord/Weird Wizard solution?
In what I guess we can call the "Shadow System," you initially choose one of four novice paths at level one: Mage, Priest, Rogue, or Warrior. You get abilities for your novice path at levels 1-2 and 5. You then choose an expert path, and you gain abilities for your expert path at levels 3-4, 6, and 9. There are a lot more expert paths (~40), including the paladin, berserker, gladiator, friar, cleric, psychic, elementalist, wizard, bard, thief, etc. Then finally you get a master path, and you gain abilities for these paths at level 7-8 and 10. There are 120 master paths in the core book, and these are a lot more specialized.
Moreover, you can also mix and match these options as you wish. For example, you don't need to pick the Priest to take up the Cleric (expert) or High Priest (master). So you could, again for example, build your character as a Rogue/Cleric/Archmage or a Warrior/Druid/Sniper.
This just sounds like prestige classes IMHO.
With the full caveat I have not investigated this system, I will address my general concern with a lot of similar ideas. If Shadow somehow addresses these, forgive me.
So, you start out with a base class: For the first few levels, you are functionally the same as every other PC of that base class. It doesn't matter that my character is a going to be a swashbuckler, gladiator, or paladin, for levels 1 and 2 I'm effectively a fighter. This is the current problem with subclasses ON STEROIDS. People already complain they have to wait three levels to pick their oath, sorcery origin, or patron. Now I have to wait three levels to even begin calling myself a paladin, sorcerer, or patron.
So now I'm level three and I'm a paladin. Great. I have the same abilities as every other paladin because oath no longer supplies granted abilities. All paladins get the same features. Granted, 5e only gives you 3-5 subclass features already to distinguish the oath of vengeance from the oath of domination, but we're effectively removing even those features. Subclasses in 5e already have to do so much lifting with so little room, they need more space to bring unique features, not less.
Which moves to part three: What is the ratio of class to subclass features. Already speaking, subclasses barely manage to add sufficient distinction to the classes as is, I could not imagine trying to fit the entirety of a monk into 4-5 levels. So on 20 levels (the classic amount for D&D) how many levels am I gaining paladin abilities vs generic warrior ones? Five? Ten? Fifteen? Five is too little, fifteen sounds like you're basically a core class anyway, and ten means half my levels are spent multiclassing into a class I didn't want to be anyway. My bard had to spend 10 levels being a generic rogue rather than being a bard.
Fourth, it forces all classes into four one-size-fits-all boxes. My barbarian has to wait three levels before getting his d12 HD. My monk has to wear armor and use weapons before he gets his kung-fu class features. My druid is casting regular priest magic before learning his special druid spells. My warlock has to have regular magic before becoming a pact-magic caster (actually, that wouldn't be so bad).
Of course, we could fix some of this by allowing the generic classes to get a bunch of customizable class features. Warriors get special combat styles that emulate skirmishing, leadership, smiting, rage, sneak attack, etc. Magic-users can pick their spell list from arcane, divine, primal, psionic, elemental, etc. We could add talent trees and feats, powers you choose every level. Those base classes become a collection of widgets you pick rather than having set features, and the subclasses give a fixed set of specific widgets tied to the theme.
But you have also just exponentially made character gen that much more complex. Rather than pick a class and have most of your choices mapped out, you are building your character every level with picking new features, preplanning paths that synergize with your choices, and watching for potentially OP/broken combos. Now, we could alleviate that by having the most common choices mapped out. Say, have the priest pick primal spells, wild shape channel divinity, and the druid subclass with the quick build "detect wildlife" and "resist poison" features. We could map them out for all 20 levels so that if someone didn't want to fiddle with charOps, they could just pick a path that has all the options balanced with thematic ties...
Oh crap, I just invented classes. Again.
Which is why I'd rather have a wide selection of already made classes so that I could go "I wanna be a knight" and then maybe a little later on decide if I'm a commander, a samurai, or a cavalier. Its not perfect, but I haven't seen a system that balances simplicity with customizability yet. Especially when all I want to do is make a paladin at level 1 and smite stuff.