>Why, for example, have we chosen p=0.05 as the threshold for approval?<
Because there is a reasonable expectation of reproducibility that has to be met. There is a good reason why scientists want something to occur with 90%+ certainty rather than, say, 67% certainty... the latter threshold would basically ensure that progress slows to a crawl.
If you go to UW and enter the Ph.D. program, and your advisor says "The basis for your Ph.D. project is an observation that we make 67% of the time that we conduct experiment X", then your best bet is to leave that lab immediately unless you want to work there for a decade and get nowhere.
There is a lot of variability in biological systems. If you lower the bar, then you're going to be chasing the inherent variability in the system rather than the biological effect.