This needs an asterisk (and I'll include one of my own: IANAL). In the United States, impersonation is regulated by the states and not consistent across them, but in general this is only true when using impersonation to commit fraud, defamation, or another act that itself is likely a crime already. Many cases would be considered parody or satire, even if no one finds them funny.

This may be the case in some places, and fraud is illegal in general, but should it be illegal to make parodies of politicians using paid actors? I think most people would say no.

Then why should it be illegal to do the same with an AI?