Thought Experiment: A Very Modular 5e

There's a lot of talk about D&D Next / 5e being very modular, where you can mix and match elements depending on the desired level of complexity.

What if character classes were extremely modular and flexible?

Essentially you'd have a giant list of 'feats' divided up into categories. For example, you could have categories like weapon proficiencies, weapon tricks, damage boosts, control spells, healing spells... whatever.

Classes would be differentiated in two ways:

1. By having a few basic abilities that modify their feats -- fighters gain greater benefit from proficiency feats while rogues gain greater benefit from movement feats; wizards add an extra die to damaging spells while clerics add an extra die to healing spells

2. By the number and categories of feats they can choose -- fighters get more proficiency feats while rogues get more movement feats; wizards get more control and utility spell feats while clerics get more healing and buff spell feats.

As an example of potential feats within the category of damaging spells, you could have an at-will fire bolt; a more powerful encounter fireball; or a very strong daily inferno. You could choose any one of these at a given level, or over time you could take all of them to build a versatile pyromancer.

At any given level you could also choose to take racial feats instead of class feats -- if you really wanted to, you could define yourself as a dwarf first and a fighter second, or the other way around.

This would give you a huge level of freedom in character creation while still allowing you to keep it simple: you could build a fighter with a lot of tactical feats, or one that's dead simple with lots of bonus damage feats. You could build a wizard who can cast a few high-power spells per day, or one that can cast many lower-power spells.

Do you think this kind of approach would work?
Would classes feel unique enough?
Would it take too much work to categorize feats and decide how many of which types each class would get?
Do you see any major flaws that I'm missing?