No, the reason Familiar used to be a shit background is it was expected to stretch "you have a mundane pet" over 5 dots. There are various ways to solve this; chop it down to a set rating, expand it into a general Sidekick background that trades the power of an Ally for having them always be around, or just offer some swankier pets than mundane animals. Revlid did as much with his
Familiar rewrite, where you got what were basically God-Blooded pets.
Lunars, meanwhile, get to turn into a t-rex
and then channel their Exalted magic through that. I think they'll deal - or at least they would if their 2e shapeshifting system wasn't a wretched disgrace.