This game still lacks pet-based champions

Because relying on AI for most of your strength really sucks.

Afaik every champ with some sort of pet/minion either was too strong/extremely unfun to play against or straight up useless because of them getting gutted.

(pre rework), and come to mind.

(And tbf I don't think that League is a fitting game for a summoner type class)

we already have supports, we dont need anymore

IMO, excluding summoner champions, the closest to a "pet system" that I can think of would be and her ball. But that's just my take.

DotA has so many illusion based heroes too. Bizarre this game has none. Not even methods of direct controlling anything other than your summoner.

Guess when the game started being developed as a more simplistic dota it was considered too complex and not fun

u mean like Rosalina and Luma from smash?