This should be the least of our worries. The incentives are set up so strongly to produce a statistically significant result that indeed nearly all experiments

This should be the least of our worries. The incentives are set up so strongly to produce a statistically significant result that indeed nearly all experiments do produce a statistically significant result. Scientists measure a data set. Then they work to find a subset of the data and a statistical test that gives them a significant result. Just ask a couple of scientists whether they ever did an experiment that didn't provide a statistically significant result. Proper statistics, where you decide on the test you'll apply and on what data before doing the experiment, is almost unheard of. And then there's publication bias, of course.