I think you'll find that the "strengthening" theory of posture is mostly spread by personal trainers rather than researchers into neuromuscular control. I would

I think you'll find that the "strengthening" theory of posture is mostly spread by personal trainers rather than researchers into neuromuscular control. I would expect any sort of mindful physical activity to improve posture to some extent, but the muscles that manage posture are not under voluntary control. Exercises designed for the large superficial muscles only strengthen the postural muscles incidentally. I wouldn't assert that AT is the "correct" way to think about anything: there are a huge number of different disciplines trying to get at the same effect with different dogmas. All these disciplines struggle with a mixture of dogma and genuine insight. Empirically, studies on AT have shown small but measurable effects across a variety of metrics including lung function, back pain, and dynamic balance. It has also been shown to reduce effort as measured by electromyography and force platforms. All these studies are complicated by the lack of a "standardized AT teacher". Most of the current research is funded by the British NHS, which recommends AT as a more cost-effective back pain intervention than surgery.