You are touching on a subject that is often ignored in medical science: the history of the p-value.

The p-value, in Fisher's view (the creator of that statistical concept), was a tool to help researchers determine whether their data were sufficiently inconsistent with the null hypothesis to warrant rejecting it.

Neyman and Pearson then built upon Fisher's work, developing what is now known as the Neyman-Pearson approach. They had the idea of not just asking whether the null-hypothesis should be rejected, but whether an ex-ante alternative hypothesis should be accepted .

They used the p-value as a pre-defined significance level (α), that is now typically set at 0.05, as the maximum acceptable probability of a Type I error. This is where the "p < 0.05" threshold became more rigidly established. Add to that the simplicity of calculating it, and what you get is medical science's obsession with it.