There's nothing inherently wrong with data dredging. Considering all possible hypotheses and keeping the ones suggested by the data is just Solomonoff induction. It only becomes problematic if you don't have a consistent prior, e.g. if you keep the hypothesis with the greatest likelihood ratio rather than the greatest posterior.

Hypothesis-driven has its place in the human practice of science, because humans have a hard time computing a prior after having seen the data. But that's a problem with the humans, not with the math.