The "one pet per character" restriction is a remnant of DOS/DOS2 engine which I hope they'll address. This currently causes problems also for using Mage Hand and a familiar at the same time, which according to PHB should be absolutely no problem.
Will also affect the [Animate Dead] spell, with which at Lv 7 you can summon more than one skeleton or zombie.
Good point about animate dead 🤔
That said having multiple summons is very powerfull. I do think they need to balance it somehow. Any suggestions?
Maybe have the limit be tied to spell cast modifier and any number above that require concentration?