Could a galaxy ever collapse into a black hole?

Yes, at least theoretically ( what else!!).

It would take a very long time, however. The stars move in stable 'Keplerian' orbits which could continue as they are for trillions of years...long after the stars themselves have burned out. But objects on elliptical orbits radiate gravitational radiation, and eventually through the very weak leakage of gravitational energy away from the orbiting stars, the orbits around the center of the galaxy begin to slowly drift inwards. Eventually, the cold stellar cinders merge into one vast 'supermassive' black hole and that is the end of stellar matter in galaxies. The time this takes is enormous...something like 10^150 years or more, so this end state is only relevant to galaxy evolution in an infinite universe destined to expand forever. Sadly, this is the kind of universe we seem to be living in!