I don’t think the OED entry for doctress has been updated since the first edition. It’s still marked as current, but the latest citation is from 1879.
I doubt doctress was ever very common, due to the simple fact that until the latter half of the twentieth century female doctors (of any type) were exceedingly rare. The OED has the sense of female academic falling out of use after 1689. The use to refer to female physician remained into the nineteenth century.
By the time women started entering into these fields in any number, feminism was going strong and they would surely object to not being given the same title as their male counterparts. The same is not true of women in the acting profession, which has had large numbers of women since the seventeenth century.
And with singing, there is actually less of a distinction between the sexes than in acting roles. The important quality is the vocal range, not the sex. Of course there are more women sopranos and male basses, but among altos and tenors you’ll get a mixing of the sexes.