I don't know of studies directly studying the vaccine for prevention of long covid, but most of the studies coming out seem to indicate that long covid is more likely in severe infections. So since we know the vaccine is good at preventing severe infections, it makes sense that the vaccine would be good at preventing long covid.

I get where you are coming from on the default being not taking medicine. But to me, I just don't see a vaccine as quite the same as medicine. It's basically a training program for your immune system. It tells your immune system what to look for and then when covid does enter your system, it is prepared and your immune system naturally fights it off the same way it always would. It just has a headstart in creating antibodies.