Would an actual pet champion work?

We already have multiple champions with pets, but none of them really has a pet as an innate part of their kit.

I'm talking more about controllable pets like Tibbers and Daisy, but used as a baseline ability instead of a powerful ult. Others have minions in their kits, but they're mostly uncontrollable (although some can be directed)

I feel like League could use such a champion, but few issues make me wonder if it would be viable, or at the very least, very hard to implement.

-Pets can interact with skillshots, so the champion's defense must suffer to compensate.

-Should the pet be fast enough to be able to dodge skillshots by redirecting it? Or slower and tankier?

-A pet that scales with the champion's speed would make it feel like you control the movement of two champions, and allow more display of mastery over the champion. But a fast pet would be really oppressive (much like old Yorick) so maybe the pet needs to be really slow early and become faster with points in an ability. Or maybe preserve the pet's speed but make it easy to trade with early.

-If abilities are actualy cast from the pet, what happens when the pet is dead? The champion needs a way to contribute on it's own at least a little, much like unmounted Kled.

-Shared health could be one way to make the pet viable, much like Soraka trade her own health to heal allies. Attacking and killing the pet would leave the controller low on hp and vulnerable. Resummoning the pet could cost hp.

-etc??? waiting for more people to point out some interesting point as to why it can't, or would be hard to make it work, or just ideas on how it could work.

Pet class/champions are a classic in many games designs, and i feel like it would be really fun to have an actual champion working like this. Even if a few champions have pets, none of their kits really exploit the pet theme to it's full potential.