Some (admittedly weak) examples illustrate this point: despite our knowledge of physics and our exploitation of this knowledge in the form of aircraft and rockets, flat-earth believers and those who don't believe/understand acceleration abound.

We know the mechanisms by which vaccines work - and could go observe the diseases they prevent by simply taking a trip, or reviewing public health data from different countries. But, anti-vaccine belief is also increasing.

There are many more of these stories, where the 'easy' idea beats out the well-established scientific consensus. Thus, I'm not sure that a fundamental understanding of how influence/addiction/personality work would change political support for these ineffective programs.

This is not true in the social sciences where it's very hard to do physics-grade research, especially given that the social sciences are very politicised, and research is often done to prove a political or moral point.

So in practice our understanding of personal and social/political psychology is pre-Copernican. There's a lot of moralising - which you will agree or disagree with, depending on your predisposition - but very little high quality research into the way that moral and political decisions are made individually and collectively.

We're left with a mythology of free objective democratic choice in politics which is clearly naive and reliably breeds monsters, but as yet there isn't a better model of choice to replace it.

I don't believe that it would change popular opinion - indeed, flat-earthers and other 'anti-intellectual' fads continue despite not being accepted by serious researchers.

The overarching goal of behavior analysis is to treat the study of behavior as a natural science. That is, to identify orderly relations (i.e., laws) between behavior and the environment.

[1]: https://en.wikipedia.org/wiki/Radical_behaviorism

This isn't any different from other sciences, where you have one hypothesis, test it, and it doesn't go the way you thought, and then people are left scratching their heads for a bit, until someone guesses right and demonstrates it experimentally.

Those mathematical models in physics you mention we accept because of debates over which was correct, for example, followed by experiments (and observations!). You see gambles on explanations of unexplained results in molecular biology all the time that don't really involve the same level of mathematical precision.

I think you're overstating the extent to which scientific process occurs in all disciplines with very precise mathematical models with low stochastic error. As the complexity of your system increases, the residual noise in any given model, especially models with little established information, will be high.