Exactly. If scientist were not concerned with the philosophy of science, they would not come up with different interpretations of quantum mechanics. There would just be quantum mechanics, and there wouldn't be the Copenhagen Interpretation, many worlds, pilot waves, etc.
The Niels Bohr quote drives this point home. Physics (and science in general) concerns itself with descriptions of nature. When scientists start to ask why, start to make interpretations of quantum mechanics, start to ask what came before the big bang, start to ask why there is something rather than nothing, that is when philosophy becomes central.
Multiple interpretations can also be useful purely as a pedagogical tool though. Using a range of metaphors to tell stories around some formal concept can make it easier to communicate and understand.
That's not to say you should assume every mathematician who communicates their ideas as though the objects 'exist' in some objective sense is a platonist, or that any scientist who talks implicitly about truth when communicating about their work, is committed to a strong philosophical stance on the matter. It can be just a habit one gets into when trying to communicate.
No doubt some philosophical remarks could be made about this too, not that I'm qualified...
The Niels Bohr quote drives this point home. Physics (and science in general) concerns itself with descriptions of nature. When scientists start to ask why, start to make interpretations of quantum mechanics, start to ask what came before the big bang, start to ask why there is something rather than nothing, that is when philosophy becomes central.