I can answer for European singers, when I’d say it might be get to be “obscene” money being paid for their work around 1690-1710.

The first condition is that we need upper-class-audience commercial outlets for music, which prior to the birth of commercial opera are essentially not around.1600s court musicians would have been well-paid, and their services were competed for among courts, but it wasn’t really “obscene” money. Commercial opera in Venice starts in the 1630s, but it’s for Carnival, it’s not a full-time industry yet. A hallmark of the careers of early opera singers is simply that none of them did it full time, opera wasn’t good enough money to be a full time living. They were court musicians first, and would occasionally get permission from their patron to do an opera or a season for a little extra cash. There’s also really only opera in Venice in the beginning, a few houses in competition, but not enough to support a lot of competition for wages. There’s also lots of courts still looking to hire these musicians away at this time, like the little German courts: Dresden, Bavaria, Bohemia, all of these would have been looking to hire Italian musicians for their court.

The second condition we need to meet is a increased demand for rare skills. The popularity of commercial opera starts to spread across Italy from Venice, and then some of the other European cities start trying to do it too. By 1690 even Dresden (bit of a backwater) was trying to do opera. For most of these cities (excluding here Paris, the French nativized opera very early) opera is going to be an import product made by Italian composers and singers. Most of musicians are pretty content to travel between Italian cities, but getting them to other places takes more money. One reason I’ve read is that the Italian roads (old Roman roads) were in much better shape than roads in other places in Europe (dirt/mud) so carriage travel was easier, but I take this with some pretzel-sized grains of salt.

But some true obscenity might have been when London tried to start having serious opera around 1720s (with Handel). Most opera singers really did not like going to England, for one, they had to travel over the Alps on a litter which was pretty uncomfortable, dangerous, and expensive. The singers were also perpetually convinced that England’s climate was going to kill their voice, or them. So getting opera singers to London took a lot of money. Getting Farinelli to London in the 1730s took 5 years of negotiations and amounts of money so obscene scholars are still debating the total damage.

It’s also worth keeping in mind that many of the people who sang in opera at this time didn’t get that much money, including choruses, ballet dancers, stage crafters, the people who made the funny hats… The high-paid singers were a minority. Most singers came from middling to poor backgrounds, worked for modest rewards, and would have known well the feeling of an empty belly. But in the end, opera singing takes a combination of rare inborn talent and long, intense specialized training. The best of them knew their worth. Caffarelli was certainly worth every penny. ;)

For a cracker-jack analysis of the economics of opera singing check out Singers of Italian Opera by John Rosselli.