It's looks like we are talking about differences of use of physics in practice versus advancing of physics as science. No doubt, if I will need to calculate something, being paid for that, I will use proven formulas. Totally agree with you at that point.
However, current major theories are in stuck, they cannot explain what we see, because now we have more data. So it is better to look for something else, which will explain everything we know already and more.
The theories aren't stuck, the existing ones cover everything we can measure, and that is amazing. Once the experiments make any new discovery which wouldn't match with the current theories the changes will be needed. So if you want the faster progress, support the experimental physics and the advancement in astronomy, don't repeat the talk of philosophers who do the equivalent to "how fairies really dance on the pin."
But don't forget: Einstein didn't disprove Newton, Newton's formulas are just a good approximation under the circumstances that were easier for us to observe. So most of what we now know will also remain as a "set of simpler models", as it is based on the valid experiments.
Yep, field is covered by formulas with pretty high accuracy. AFAIK, the only practical field when correction is needed is GPS satellites, but correction is extremely low. However, our vision is moot. Video above just opened my eyes.
However, current major theories are in stuck, they cannot explain what we see, because now we have more data. So it is better to look for something else, which will explain everything we know already and more.