They are unpopular, even hated now. Some have been hated for long enough that they are so out of fashion that people have forgotten they existed. If you called a female MD a "Doctress," when she figured it out at all without hints she would think you were being funny or clever. Perhaps not successfully funny or clever, but it would be so outdated as to not even be on the radar. Yet when it came in in the 19th C, many women insisted on it. "I want people to know that it's possible for a woman to be a doctor!" Or, I conclude, a poetess, songstress, authoress. The thinking was, if you just said or wrote "doctor" everyone would assume it was a male, and men would get the credit for what women had done. She, a woman, had succeeded and she wanted it noted.
The suffix -enne is similar, but little used.
Two words seem to be exempt from this current deploring of feminine forms of nouns, goddess and actress. "God" may get the edge as a more important form than the feminine because of a thousand years of Christianity in it, but in the pairing "gods and goddesses I don't think anyone is perceiving an inequality there. Also, some form of feminine expression, even if it is as a hunter as with Diana, is often considered central to the goddess's identity. She makes things grow. She cures diseases. No one is likely to look down on those things, and may even consider them more important than whatever the sky-god is doing at the moment. Why actress has held up without attracting ire I'm not sure. That it compresses attractively surely helps. If actoress had been the form we developed that one would be on the chopping block now. It may be that because this was one of the first previously-male occupations that women established themselves in (for obvious reasons) it has just become a word. We think of it as the twin of actor, not some patronising affair. Also, as with goddess, the specifically feminine characteristics are not incidental to the task, as they are with doctors or authors. There are no generic gods, and there are not any generic actors, though the gender boundaries are increasingly porous there. And I have heard that women insist on being listed as an actor on the assumption that there must be something lesser about any feminine form. I think that is artifical and not really in our associations. Yet if disapproval of the general category of feminine suffixes eventually wins out, that will go out with it anyway.
The suffix came into English attached to nobility, as in princess, duchess,or baroness. These were usually the wife of the title-holding baron or prince, but sometimes the woman came in with the title on her own, and her new husband picked up the title Duke from her. It was not regarded as a patronising or especially lesser version of the masculine title. In practice, it may have carried a bit less power, but that is not easily discernible from the written record. "-ess" does not have to mean a lesser form, it has usually just meant a female form, no prejudice. If it carries an air of the patronising now, it has caught that from sexism, it was not the cause. It is the cart, not the horse.
"-ette" is different. It is clearly not only female, but describes something as smaller. Smaller is not always lesser, but that would be the way to bet. Suffragette was originally given as an insulting, supposedly humorous term, but as often happens, as with Quakers or rednecks, the victims laughingly embraced it and made it their own. We don't think of suffragette as "oh, the little woman has taken up a cause this year, how cute" anymore, it's just their name, fairly neutral. The same with majorette. We can think it back, especially if we were in band or went to a large university, that there is a drum major who is a big deal, while there are collections of lesser majorettes, but that isn't our usual first association. It's the word for a girl twirling a baton. We have to work to even think there is a male equivalent.
"-ine" is largely in proper names. In a great many languages of the world, not just Indo-European ones, the "-a" suffix denotes the female. There is usually a corresponding masculine suffix, so there is no sense that women are being singled out as having to be noted as some exception. Antonio, Antonia. It was Paulus, Paolo for males, so the ending of Paula is not some tacked-on bit. In English it does get that flavor, because we ripped out the endings in a lot of places making the masculine form look like the "real" one, so Robert, Roberta; Gabriel, Garbriela. But English is very unusual in that. "ina" is a combination, usually coming in with foreign words like "ballerina" or "concertina."
The last is "-trix," which was never common. My mother was executrix over the estates of her mother and some aunts in the 70s and 80s and I just got used to the term as a simple feminine, certainly with no diminution of role implied. I think I have occasionally used the term. I am told it is now incorrect and out-of-fashion. Well, fine. I can't see that it matters one way or the other. I'll adjust. Aviatrix is now passe, but then aviator is not far behind it anyway. The only remaining common usage is dominatrix, which is so sexually charged as to overwhelm other associations. If you put that suffix on a noun to refer to a woman now it would not be perceived as a slighting, diminishing expression, it would be instantly processed as a sexual, likely humorous one. No, I am not going to make up an example here. I don't want to start any unfortunate trends.
Thus here we are with a new language cause to enforce. I don't much like enforcement in such things. Once people get the idea they usually shade to the newer, preferred cultural meaning on their own, without self-appointed language police requiring it.