No contest that relying on unpaid labour is awful. But "obscenely rich"? My overwhelming impression is that despite all this, no one really gets rich on running restaurants. Certainly not when you factor them going out of business all the time (or even falling out of fashion, that's basically death for a Michelin starred eatery).
Simple napkin-math from when I was at the restaurant. I.e. multiplying the amount of people at restaurant by the number of days in a year they were open, multiplied by how much one of those "tasting menus + wine pairing" cost (which almost everyone buys); would suggest that their revenue would be somewhere in the range of 20-30 million dollars in revenue a year. That restaurant is always full, I think we booked our table 6 months in advance.
Clearly they serve you expensive wine, and a lot of expensive produce goes into their food making. But I would guess that the main cost of running that place would be the cost of paying the employees; which they don't. That 3-star restaurant (and many others), are making their owners extremely rich.
The restaurant business is extremely competitive, and most businesses struggle, but some are making good money. I live in a small town in Norway (200.000 inhabitants), and even here there is a guy who runs a bunch of restaurants, with profits in excess of 3 million dollars annually.
If you want to make it big you need to treat it like a business, like Gordon Ramsay does. He owns 23 restaurants (maybe more) all over the world, his name is known by many, and the income from tv-shows would pay the bills by themselves; they also serve as advertisement for establishments with his name attached.
The few restaurant owners I know who make a good income here in Amsterdam tend to own more than 5 restaurants. Some have their own branding going on, some just take care of the business side of things. And even then I think it's a whole lot of work and stress for relatively little pay.