Those models aren't worth much if you don't test them, so these efforts will have to go hand in hand. The way it tends to go now is RCT -> try to explain findings by hypothesizing about mechanisms -> think about an RCT that can test this hypothesis -> repeat. It's a slow and expensive process and not always successful, but I would say that it's progress.

I would say testing is a small part of building models: building models should essentially be driven by theory, not by experiments.

Stare upon the FRBTheory wiki in delight then, here are ~50 different theories describing the same thing: https://frbtheorycat.org/index.php/Main_Page

As a generous guess at most 40 of these models are wrong, since they all describe basically the same few events with vastly different mechanisms. I guess that majority of interesting but wrong models is what you are after?

The space of incorrect-but-reasonable models is infinitely larger than the space of correct models. The way to distinguish between the two is experiment. Experiment is therefore the much more important side of the balance.

Uh, have you heard about Astronomy at all? Admittedly it's purely observational measurements, but you'd need a very poor philosophy of science to deny that the careful measurement of radiation is not an experiment.

As for trials, the universe itself has provided billions upon billions of different objects to perform measurements on.

There's the "shut up and calculate" thing within particle physics. I don't know how seriously it's taken.

What? Shut up and calculate is an interpretation of Quantum Mechanics in general, and is probably most common as a backup to the Copenhagen interpretation.

It doesn't have much to do with theory building at all, as most theory involving QM doesn't need to concern itself with exactly why QM works despite its strange philosophical meaning.