Short answer: the methods used by the Postural Restoration Institute work and have been adopted by many of the best physical therapists and athletic trainers in the country. It is an evidence-based approach.
Slightly longer answer: my limited understanding as an outsider is that PRI techniques have come under criticism by certain physical therapists who are unwilling to accept that they are wrong about some fundamental truths about anatomy, neurology, and the nature of pain. It is largely a political problem within the field. As the body of evidence supporting PRI's claims and techniques have grown, these criticisms have become less common and less credible.
My personal opinion is that the "mobilize this side of the joint and strengthen that side of the joint" approach to addressing movement issues has gained so much traction (at least within the fitness industry) because it is relatively simple to understand and, accordingly, use to position yourself as an expert on the internet. It is easy to write an article about how you should stretch your hip flexors and do glute bridges, and at the same time it makes you appear relatively knowledgable to the uninformed. I believe this is why people within the fitness industry like to write such articles, and why that school of thought has become ubiquitous.