Wasn't there some DM minor-celebrity-figure who a year ago came up with a system for turning literally any monster (in O5e) into a pet? Didn't it include rage dice, something like that? I'm pretty sure in the same third-party sourcebook he published he included a class entirely focused on maximizing the use of such pets.
I love the idea, and if such a thing existed for A5e I would use it. I do think it's worth noting that there is a greater degree of convenience in an archetype that says, "Hey, here's a wolf that's your friend. It gets stronger in these ways as you level up. Now just go play the game."
Also, just my opinion, I think it's easier for an archetype or class feature to grant a minion that feels like an extension of the player or that naturally synergizes with the player character's abilities than a separate, universal system that anyone can use. But for people who like their pets to feel separate or do their own thing, that doesn't really matter much.
In other words, both ideas fill different "this is how I have fun" needs.