I still have to disagree that the movie MUST be filmed in NYC. The argument is working under the assumption that the movie would be filmed
on location, should it be filmed in NYC, which would have likely not been the case. It's very expensive to film on location, especially in NYC, and particularly for a film of this nature (with the lip-syncing, the choreography, the style, etc.), time and budget constraints would make filming on location prohibitive, not to mention each day would have to be rushed to meet these limitations and we wouldn't get he perfection we expect.

There's really no difference whether the interiors of the film are shot on a sound stage on Treasure Island or a sound stage in Queens. Either way, it's going to look and feel the same.
Now, if the major exteriors were to be filmed in SF, and if I see the Golden Gate Bridge in the background, that would be a different story. But I think we should relax about having the interiors shot at an SF studio.
It's all going to look the same. Just my $0.02. (Canadian currency, so it's not worth too much.

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