Why would "actor" require a female form, when "doctor" does not (at least in English - dottoressa is a thing in Italian).
There's are two inter-related historical reasons, unlike the medical field in many societies, acting has had men and women participating heavily in it since the 1600s.
Second is that for occupations that have been historically male-dominated, "doctor", "lawyer", etc., once women starting working those jobs, they are pretty much doing the same things as men. Assuming your not a sexist, your going to believe that a female doctor is qualified to all the things a male doctor can do and vice-versa. But in theatre, there is still a gender separation because it generally determines what roles you'll play. Even today, when "cross-gender" casting has become somewhat common, you still can't do it without being seen as "making a statement."
I don't know if that makes sense to anyone except me, but yeah. Also those are just historical reasons for why the language is like that, and doesn't mean we still need separate terms today.