I've heard that idiom, and I'm sure it has its use. I don't think we should stop calculating, by any means. However, there are individuals in the field who think new insights are possible through continued attempts to improve our interpretations (in addition to continued development of the theory as expressed through robust math). I don't have a source handy, but I've heard the physicist Sean Carroll express this idea on his podcast, Mindscape.
Numbers by themselves don't mean anything (for humans at least). The meaning is found in how the numbers relate to the concepts that we make use of.
It is legitimate to ask how our everyday perceptions can be so radically and fundamentally different from what the math appears to say about the nature of reality. "Shut up and calculate" is not a legitimate answer.
(For the record, the phrase "Shut up and calculate" was coined by David Mermin as a pejorative characterization of the Copenhagen interpretation, which actually says simply that we cannot know anything more than what the math says, and that's just the way it is, and any attempt at further inquiry is doomed to fail and therefore should not be attempted. It's a deeply unscientific attitude.)
I read statements from Feynman that I interpreted as very similar. He said things like: the question "what is the underlying reality behind all this" probably "has no meaning." I never understood what he was trying to say.
Numbers by themselves don't mean anything (for humans at least). The meaning is found in how the numbers relate to the concepts that we make use of.