For someone who claims to dislike elves, this certainly makes them a better option than many races.
Spellcasters able to fight decently without casting spells will be the best choice: Bladesingers, Valor Bards, Swords Bards and Moon Druids.
You'll be up to your pointy ears in trilling fops, and furries.
Any other casters will have to make sure they get a decent ranged and/or Finesse weapon from their race in order to have an effective action during combat. The sort of race commonly found frolicking through the woods singing roundelays.
Also Paladins. They can burn their spell slots just fine, and laying on hands isn't a spell, so they're good there as well. These rules aren't going to limit your average elven paladin when they can just smite away with both rapiers just as soon as they mince up to their opponent.
So Elves and Bards are like the Dark Side of the Force. It's the power that tempting; never mind the evil. No matter how much you try to tamp them down, they will still be there. Doesn't give you license to succumb and murder all the younglings.
But I am relatively unworried about the idea of people making spell casters that are competent in melee without spells. That's the idea.
The issue of half-casting melee classes (Paladin, Ranger) is something I haven't really thought about yet- I think many people enjoy the various ranger variants that do not have spells for a reason. As for Paladins, the issue is primarily smite; honestly, other than not allowing smite but continuing to allow them to use spells for other reasons, I can't think of a better proposal. But that's why we have the wisdom of crowds, right?