SR has limited applicability it is a theory about a non-expanding spacetime geometry which has no curvature. This is not realistic. But SR is very useful in any situation where the curvature is almost zero and the expansion is so slight as to be negligible.
The trick is to know when NOT to apply SR and when NOT to expect it to give reliable answers. It is after all only an approximation to the real geometry.
SR works best over relatively short distance and brief timespans, away from very massive objects.
GR is apt to work better on large (like intergalactic) distances and long (cosmological) time scales. But all mathematical models are only approximations and must have their limits of applicability. Even GR fails if pushed too far, as to the center of a hole or back in time to the very start of the bang. There is always room for improvement of the models.
A nice thing is that GR RETAINS ALL THE GOOD STUFF OF SR, because it has SR built in to its local coordinate patches---ready to serve as a useful local approximation. So when one moves up to the more general theory one does not have to GIVE UP anything. One just gets the same SR stuff but in a more complete context with the additional ability to describe curvature, gravity, expansion of distances etc.