If you can't make useful predictions within the parameters of your model, you can't test the ideas. Ergo, the shut up and calculate side does have a good argument.
Previously, in physics, there has been a three-way dance between theorists who develop the mathematical description, theorists who develop the mechanical description, and practical physicists who carry out observations both to test the theories and to apply them in practical terms. This dance kept everything moving.
This may or may not be the correct way to approach quantum mechanics. The rules are very different in that domain.
On the other hand, it's easy to spot the hostility between the groups and it's obvious that the anticipated new physics isn't getting found. New models are rare and are struggling. The dance hasn't completely stopped, but it is definitely in trouble.
But, of course, that might equally be down to the increased competition, the need to publish trivial results quickly rather than do anything profound, and the greatly reduced investment in blue sky science.
I'm going to suggest it's a mix of stuff. We need a lot more funding, a lot less aggro, and we either need to get the mechanical description partner back on their feet or we need to find an alternative to them if that sort of description just doesn't work in this arena.
But I think the science dance needs three sides. I think we're going to find that the calculate lobby can't advance a whole lot further on their own, and that they cannot produce a theory of everything without some idea of what an everything is.