As someone who's been close to several opera singers (long story), I would say that the amount of opera singers who don't have side gigs in teaching or otherwise is very, very small.

Yes, if you're one of the few world famous sopranos you don't need to teach, but most singers are not world-famous. I knew one singer who toured internationally, had sung in front of thousands of people, had sung with world famous people, etc. But who lived in shared accomodation and worked several other part-time jobs to make ends meet.