Newtonian physics looks kind of logical. It's completely wrong, but plenty of decisions are based on it. Despite that we know is wrong
It's not *completely* wrong.
In fact back then when it was discovered, it was experimentally proven to work within the parameters which were tested.
The reason it was used then and is still used now is that within this range of parameters, it still works. For everyday use, what newtonian predicts is within what is observed. That's a precise enough model.
What happened is that scientists started to consider much more extreme paramters range (higher energy, faster speed). At that point, newtonian physics breaks down. Does it mean that all the past results were wrong ? No it simply means that it's a model which is only works within a certain range of parameter (it's good for everyday use - you car) if you need to consider parameters outside this range (space ships, planets) you need a better model (general relativity, etc.)
- with Newtonian physics we speak about a physicis model. About a model that's used to approximate real-world events. This kind of things only get experimental proof (prediction fits the measured data or not). And will eventually get superseded by a better model which works better including for some corner cases or at higher range, smaller scales, etc. (String theory and such were born as a tentative at a better model than the dichotomy between relativity and quantum mechanics).
- with TFA: it's a bout a *mathematical proof* that 2 different models are really actually the same stuff just expressed in different ways. Take one model, tweak the equations, and you should obtain the other model. It doesn't speak about the quality of the models themselves, just the mathematical links between them.
(I fact, the quantum mechanics model has its limitation - what you call "wrong" and what I call "use it only within the range of value where it works the best.
QM works best at predict very small scale phenomena (particles, waves, etc.). QM completely sucks at being useful for anything at the other end of the scale: QM is a piece of shit for astronomy. And vice versa: relativity is good when you consider stars, useless when you consider particles. 2 models, each best at a different scale. And strings being a possible future model that could simultaneously work at both scales.). ...but usually, when you have a newer model, that is better experimentally, you usually also need to find a mathematical "link" between the two, an explanation why the old model used to work and only got contradicted in your experiment.
e.g.: take the relativity equations, and use them to compute the motion of your car - the level of energy and speed are so small, that all the "weird parts" of relativity can be approximated and rounded to 0, what remains ends up looking exactly like newtonian physics. Newtonions physicics are the same, simply with the relativity parts neglected, because they don't play any significant role at that scale.
Science constantly bases decisions on kinda logical principles until those principles are proven to be wrong.
Newtonian physics looks "kind of logic" because it's a model designed and tested and proven to predict a range of events (reasonable speed, low energy, human-size scale instead of particles, etc.) which happens to match what our monkey-brain have evolved to cope with.
(our ancestrors never had to think about nuclear bombs, supernovae, tunnel effect in electronics, etc.)
That's also why it got discovered first (we didn't first invent relativistic physics and the newtonian as handy simplified formula for some type of problems), because that's what was easiest for our monkey-brain to think about.