>>96468836
First problem is having pets at all, most systems start grinding to halt or completely falling apart the moment number of combatants reaches double digits, having pets adds up to that.
And no, this isn't specifically just DnD problem, I'd rather re-do my whole college entrance exam than calculate ricochet of projectile blind-fired into furnished densely populated room in GURPS ever again.
That said, if you wanna have pets anyway, there's two ways to go about it - individualized pet with deep personal connection, that will always be your +1 and never more than +1 (like Drizzt's panther). Or random number of disposable ad-hoc shock troops that are only available sometimes (like Squirrel Girl's gimmick, or any random crazy cat lady). The prior runs into a problem of narrative justification of making the pet persistent and always available - even in urban areas, or in the middle of a dungeon - and some amount of handwaving of bringing it back should it ever fall in battle (or into a pit trap). The latter is more difficult to balance and can easily become useless or too damn busted. Flock of eagles won't do much good underground, but could be excellent counter for flying enemy.
Ranger thematically fits the ad-hoc summons, but most players will usually want a persistent pet then piss and moan when it eats one too many fireballs.