I'm sure you're right about the original use/meaning, since I imagine the word was used long before there were any female mayors.
It was. And in that context it worked just fine.
However, in terms of accepted/acceptable current usage, dictionaries (including OED) seem unanimous in including both meanings, without any comments I've seen suggesting that use of the word for female mayors is undesirable.
It's clearly undesirable, as it immediately creates problems.
It is wrong-headed, illogical, and arose because of ignorance of the fact that the word "mayor", per se, did not in any way mean a male holder of the office.
Between 1992 and 2000 Betty Boothroyd was not The Speakeress.
Between 1979 and 1990, Margaret Thatcher was not the Prime Ministeress.
Whilst retaining the term "mayor" for female office holders would have done nothing about the problem of what to call her spouse, changing it to "mayoress" did nothing either.
It was pointless, and it was unnecessary, and it was done in ignorance.
It was wrong, and the fact that it has become an established usage does not change the fact that it was wrong.