I like how the Necromancer works in 5E.
As he levels up his (new) pets get +1 hit point per level more and do + proficiency to their damage. He controls all (or some) of them with a bonus action, so if he has 2 skeletons and 2 zombies and he wants the zombies doing the help action and the skeletons doing attacks, it takes 2 rounds to get all of his commands going and by then, the situation has probably changed anyway.
I think that a class feature that increased the pet's hit points (maybe +2 hit points per PC level), damage (+ PC proficiency), and to hit (+ PC proficiency) would be sufficient. The pets saves still suck. Its AC is still low. It gets hit a lot and takes damage a lot and misses saves a lot, but it can still fight and hit somewhat frequently and do some decent (but not great) damage.
The PC then has to use a bonus action to command the pet and the pet does not always understand the command.
Plus, spells and other things can confuse the pet. For example, if the PC wizard shape changes into a troll, the pet might just go attack the troll if the pet is guarding an area and the troll move in. In the pet's mind, this troll invaded his guard space. Attack.
Game elements like this (some minor level boosts plus some restrictions on actions) would tend to keep pets balanced.
As he levels up his (new) pets get +1 hit point per level more and do + proficiency to their damage. He controls all (or some) of them with a bonus action, so if he has 2 skeletons and 2 zombies and he wants the zombies doing the help action and the skeletons doing attacks, it takes 2 rounds to get all of his commands going and by then, the situation has probably changed anyway.
I think that a class feature that increased the pet's hit points (maybe +2 hit points per PC level), damage (+ PC proficiency), and to hit (+ PC proficiency) would be sufficient. The pets saves still suck. Its AC is still low. It gets hit a lot and takes damage a lot and misses saves a lot, but it can still fight and hit somewhat frequently and do some decent (but not great) damage.
The PC then has to use a bonus action to command the pet and the pet does not always understand the command.
Plus, spells and other things can confuse the pet. For example, if the PC wizard shape changes into a troll, the pet might just go attack the troll if the pet is guarding an area and the troll move in. In the pet's mind, this troll invaded his guard space. Attack.
Game elements like this (some minor level boosts plus some restrictions on actions) would tend to keep pets balanced.