Consider that a lot of players already expressed they wish that cavs in general get nerfed. Some ideas where to decrease speed as we're talking above but also make cs cav 2 pop and 3 for champs... Theses ideas would nerf cavs much more then making their counter actually works. I also agree with players saying that cavs should ideally be an auxiliary force of an army and rarely it's main force. So even if you invest more to make cavs, you aren't guaranteed to be able to take out a similarly sized inf army. Cavs can already choose what fights to take or not which is their core strength in the first place, and alone could justify a greater price.
Beside the fact cavs can hardly be caught by inf spears cav have a lot of extra hp:
Cs melees cavs have x1.5 (1.6 with Horse breading) of melee inf
Cs ranged cavs have x2 (x2.2 with Horse breading) of ranged inf
These hp make them tougher to projectiles, but also spears x2.5 counter was making them barley catch up with the extra hp...
From here I'll be in favor of making melee cavs roles more defined. Spear cav could get their damage against other cav increased, and sword cav could benefit from more pierce armor for them to be more effective when trying to kill ranged units or raid enemy base.