First, there's nothing wrong with class proliferation for extra experiences.
Yes, but there comes a point where you are potentially sacrificing replay value. A class with many options can encompass all permutations of those experiences, and is more practical if you don't want to take up book space to turn each permutation into its own class.
Second necessity is the mother of invention. If we want the benefits of freedom and creativity let's throw out the entire 300 page rulebook that is the PHB. And the DMG. And the MM with it. On the other hand restrictions can drive creativity. Present me a blank sheet and I don't know what to do with it. Seed the water with ideas and I have dozens that build off them.
Reductio ad absurdum? It has its place, but I don't see much value in this case.
Let's take a more reasonable example. What would happen if we eliminated the class spell lists and any spellcaster could pick any spell?
In the pro column, spellcasters could be tailored to match a concept more easily. My wizard might be a white mage, casting healing and support spells without the clerical baggage (such as having a deity).
In the con column, differentiation between the spellcasting classes would be significantly watered down. You could have rangers tossing fireballs, and fiendish warlocks conjuring angels.
Now, I'm not advocating no class spell lists. While I would love the ability to play a red mage in D&D, I freely admit that it's not a core D&D class concept. However, as I hope you can see from the above, there are both advantages and disadvantages to any approach. More classes with more restrictive spell lists is certainly an option, also with pros and cons. Personally, I prefer the former. I'd rather pick from a spell list to turn my wizard into a fire mage, rather than having to wait for WOTC to produce an official fire mage class. Having options is good, although there do come diminishing returns at some point.
While I realize you might disagree, I think the system as it currently stands is a fair compromise between creative freedom and restrictions.