The alternative is to stop testing a default "nil" hypothesis and instead come up with various mathematical/computational models for the process that generated

The alternative is to stop testing a default "nil" hypothesis and instead come up with various mathematical/computational models for the process that generated the data, then test that on future data. The model that makes the most precise and accurate predictions with the least assumptions/complexity should be used until a better one comes along. This is quite honestly just how science used to be done before NHST. It still is done this way in many areas of physics and engineering.