There are plenty of shuls where the rabbi is a bachelor. A good friend of mine was a single rabbi in Long Beach for a few years, the rabbi of the Stanton Street Shul (another friend) is single, as is the rabbi of the West Side Jewish Center (yet another friend). Many rabbanim won’t give semicha to bachelors, since the single life is not looked upon favorably by our sources, and the Gemara speaks of instances where bet din can compel a man to marry.
I don’t see how a rebbetzin is crucial to a shul; he’s not leining, she’s not leading tefillah, and in most cases, she’s not giving shiurim. A rebbetzin could be a vital asset to the female members of a shul, and can serve as a conduit to convey she’eilot about niddah issues, but I don’t see how the rabbi’s wife plays any key role. The rebbetzins I know generally support their husbands, redt shidduchim, help make kiddushim in the shul, sheva brachos for mispallelim, other simchas, etc. But most rebbetzins are not Esther Jungreis or Tzipporah Heller.