You certainly can't have infinite hotels in physics, but it would be incorrect to assert that we have any good reason to believe that infinite quantities can't exist in nature. For instance, the model of the universe most widely accepted by cosmologists today implies an infinite universe, assuming that our measurements of the curvature of space are correct. And these cosmologists don't believe that these infinities are just a mathematical artifact. Rather, they believe that the universe is likely to be infinitely large, in actuality.