Yes they can just go bad. I highly recommend an AC Delco. The one I bought has a Bosch motor. They are know for being one of the best fan motors. Maybe they just last forever, I dunno. My old Mercedes had Bosch fans and still work. I will say the AC Delco fan works better than the crappy one that was on the car, made in Taiwan. I think the AC Delco was made in Mexico. Motor made in Germany.
Check temp switch for voltage across when up to temp ( test on stove in a pan of water) could be a bad ground I had that problem with temp sender .Check fuses? Jump 12 volts to fan see if it comes on if not it’s bad