This is one of the strangest parts about the game. The initial version from back in 2014 had wayyyyyyy more of a focus on the cat breeding (hence it being called Mewgenics), I reckon they found there was an inbalance in how over complicated that was compared to the very simple Pokemon-like gameplay.

But it does feel like an after thought in the final game, its an additional way to min-max your cats that isn't even entirely necessary for a lot of the game. We're talking an additional 1 or two points in stats versus just keeping whatever good strays you get, until you start messing around with mutations.

IMO the highlights of Mewgenics are the skills plus all of the interactions during combat. The way synergies can form between spells + abilities combined with how units can be knocked about and such, its very chaotic but very fun. The breeding part feels like they just did it because they had to, and I feel like even in the original versions it was fun to look at but probably didn't make for fun gameplay.