Modern medicine is hardly logical where therapies are concerned. There is often not any coherent theory of why a therapy works and yet it may be commonly used in treatments. If you examine the literature supplied with your drugs, it often states "exact mechanism of action is unknown but yada yada". This is why there are double blind studies in medicine. Absent a theory, this is the only way to gauge the effectiveness of a therapy. Hence, if bathing in slightly radioactive waters has provided beneficial to people over a long period of time, you can't dismiss it as "appealing to tradition". It may need validation with a study but can't be ignored as just tradition.
The fact that it's been done over a long period of time does not prove that it's beneficial. As you say, that's why there are double-blind studies. If the only evidence of benefit is that it's been done for a long time, that literally is just tradition. It's worth looking into it to see if it works, but there are plenty of traditional remedies with long histories that don't.