It absolutely does affect the predictions research makes, because funding and PhD students are assigned to whatever models are most popular at the time. For a long time that was string theory, and a lot of departments considered other approaches to be non-optimal for career progression.

Which sounds fine if you believe that heterodox but still valid science gets into the mainstream eventually - like (e.g.) the theory of continental drift did.

But what if useful science falls through the cracks? What if we could have had a valid theory of quantum gravity by now, from a left-field approach that never had funding or PhD students to research it?

How would anyone know?