For one thing, it has a very negative impact on a sense of progression and player buy in. Nobody likes having to balance 5 different unexciting feats, races, and class features. It makes the game overly complicated and messy.
People should be excited to take an option. Flipping through page after page of boring options that give you +1 to save DCs while doing backflips next to a goblin isn't going to do that. In fact it's going to do the opposite.
Please, PLEASE make the base feats in the core more interesting, especially at low level. So many are so terribly boring that they should be thrown out.