I don't see why the wife of the "incoming" king wouldn't always be titled Queen Consort as a matter of course. So, yes.
Conversely, I think it's kind of sexist that a regnant queen's husband is almost always relegated to the title of prince rather than King Consort.
A King is per definition a monarch so that is a no-go. A Queen is normally a consort and other languages than English use some form of "reigning Queen" for a Queen who is a monarch herself.
If we're going to continue to have monarchy as an institution in the 21st century, I think we can accept that a country will not always have a man be its head of state and that if a queen can be regnant, as is the case in most European monarchies at this point, you can just as easily have a non-regnant king.
Virtually everyone in Europe accepts that a Queen can be regnant, but the title of King is not and has never been a consort title. Queen and King are not similar titles. If you want to make the terminology gender neutral it would make more sense to allow a woman to become King.
I don't know the etymology behind "king" versus "queen" in Germanic languages.
The Latin "rex" and "regina" both come from the same root word. They essentially are the same word gendered differently. So I don't see why there would be any inherent implications in the male version of the word that would not be in the female version, apart from social/cultural assumptions that are no longer relevant in the modern era.
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