Relativity is not hanging on just one or two experiments and has made tons of testable predictions.
If better theories are already properly developed and can explain observations and testable data with the same rigor, reliability and consistency as the currently accepted theories, it will not be long until they become the norm, much less than generations. That's the nature of science and that's what everybody in science is after. Nobody is running away from it, is just that the explanations you are talking about are not as convincing as you think.