I don't think I'd like it. Good arguments explained on Devalue's post.
It would make chaotic scenarios with way too much stuff going on simultaneously more frequently, making battles unnecessarily
convoluted.
And it would potentially break the game even more by overpowering those Pokémon that have two/three amazing Abilities but normally have to choose one (Azumarill, Krookodile, Bronzor, Frosmoth, Excadrill, etc.) while hurting Pokémon that have one useless or extremely situational Abilities such as Houndoom, Starmie, Shiinotic, Ribombee, or Camerupt to name a few.