It removes much of the front-loading of races. It removes the obvious racial choices. No more is half-elf the go-to choice for the Paladin or Bard, for instance.
also @Horwath whose post above is the better solution if you want to do something about it with alternative rules for the stats:
Your intention is an interesting take, I guess your players are into minmaxing and optimizing, see one thing I do houserule at my table concerning stats is the old 3e rule for a spell of level x you need to have casting stat = 10+x, maybe that one helps you a bit. so wizard who wants to cast 5th level 15 int minimum that is.
(So no EK with Int 8, that guy cannot even "spell" his name in my games)
Also for armor, I enforce the STR rules, or in my current campaign there is also a full plate available needing a STR of 18 for a AC of 19.
The following is depending on what your players would accept, just make the optimum combos not available in your next campaign. Sorry now dwarf light domain cleric e.g. No half elf at all in this world, they all died/humans +elves genetically incompatible or what you have.
There are optimum combos in 5e RAW that is clear, but if you still need to go by mainly RAW concerning fluff because you have a younger PC group who just cannot accept that a dwarf never can be a wizard, then eventually introduce RP reasons to not take the optimum, like communicate to your player:
Sure you can play that half elf paladin, but know this: He is shunned in both elven and human society, the humans will consider him an atrocity of nature and the elven as an impurity to their race.
You still want to play that character? Good, but I warned you upfront.