Honestly in retrospect, that would get people panicking, wouldn't it? The only reason you'd be looking for Case 53 samples would be if you were wet-tinkering or tinkering things that affect powers. Both of which would get much attention, especially from Cauldron. Sure, people were already suspecting him of doing that kind of things, but while Weld's sample can be explained away by just wanting living metal for something normal Tinker-y, collecting biological samples and data is a big red flag for that kind of thing.