So just as am fyi the new basilisk warrior can get a pet basilisk. It is an addition to the class and not the man focus but it hasn't felt more powerful than any other class I have seen played.
I will admit, I was pretty hyped when I saw that as an option. Even though it's not really what I'm looking for, it's a step in that direction—although my excitement tempered as I realized how limited this feature really is. I wish there was an option to "age up" the pet basilisk, make it stronger, as you level up—if you roll "12" again on the talent table, maybe.
Also, I prefer to play the game very strictly, so the odds of me ever getting such a basilisk egg are pretty low—I almost never roll a "2" when doing my talent rolls.
It doesn't have much it can do, it has the chance to turn people to stone ... Slowly and can make a weak attack. The player controls it completely. The main class is more about having natural armor and a petrifying gaze of your own, the pet is a talent you can role so it is not a big focus of the class.
Which is part of the issue (for people like me). It feels like an extra, not a core focus. I also don't like that if the basilisk dies there's no built-in way to replace it (even if that means waiting until you can go to town and find a new one to train), which means you need to buy one, or go on a quest for it—which anyone can do, it doesn't need to be a class feature, and it's a real hassle.
The nice thing about minions as class features is it means I have that as a built-in option when I want to play one—I don't have to hope that I will survive long enough to have the money to buy one, or the levels to survive a quest for one, and I don't have to hope that the GM is willing to play ball in the first place. I get to play the way I want out play out of the gate.
Granted, Shadowdark
kind of has pets/minions as a core feature built in some classes. There's the Camel Rider and the Kyzian Archer classes. Naturally, those are very focused on the minion as a mount, rather than as a skirmisher, tank, or utility focus—so also not quite what a pet master/puppet archetype invokes, but kinda getting there.