Is it? I think that the most widely accepted interpretation among physicists is the shut-up-and-calculate interpretation.

There are quite a few people that actively do research and debate on QM foundations, and, among that group, there's honestly no preferred interpretation. People are even looking for alternatives that bypass the problem entirely (e.g. GRW. The debate is fully open, at the moment.

Outside of this specific field, yes, it's pretty much shut-up-and-calculate.

Yes, doing the calculation and getting the right result is worth of many interpretations, if not.all of them together.

Besides, interpretations usually give you more than the truth. What is awkward.

The wikipedia page on the Copenhagen Interpretation says:

According to a poll at a Quantum Mechanics workshop in 1997,[13] the Copenhagen interpretation is the most widely-accepted specific interpretation of quantum mechanics, followed by the many-worlds interpretation.[14] Although current trends show substantial competition from alternative interpretations, throughout much of the twentieth century the Copenhagen interpretation had strong acceptance among physicists. Astrophysicist and science writer John Gribbin describes it as having fallen from primacy after the 1980s.[15]