Agreed. The basic premise is that everyone brings something different to the table - different focus, different abilities. Even in circumstances where everyone chooses to be the same race and class, 3.x and it’s persistence with using die to determine abilities meant each character would be different.
I agree that there were a lot of skills in 3.x and the choice seemed daunting but not each class got the same number of skill rank to allocate to a skill at each level. For instance, Bards generated lots of skill ranks that they could use untrained and a lot of skill ranks to be allocated for each level (6+Int). Wizards, by comparison had a mere handful and few skill ranks to be allocated.
Some skills in 3.x could use the take 10 and take 20 mechanics. It allowed a partial roll on take 10 - that is 10 plus your roll to ensure greater success - and take 20 that if you spent time and effort you could forego the randomness of a roll. The Take 20 was useful searches and healing for everyone. As the PHB, said though, take 20 was not useful in all applications. For instance you couldn’t take 20 on the move silently skill to sneak up on a hobgoblin guard.
As for the OP original view, yes in IMHO 5e should have better adapted skills and not effectively dumbed them down to the point that they are. They are generic now and not really meaningful in creating sufficient variation between characters. I also think the fortitude, will, and reflex saves had some value too - particularly to ensure use of what are otherwise now under-utilised abilities (ie, Con and Int).
Well, that seems not to far off what PF2e is doing.