> It's not acceptable to prohibit a use case because some people are using it for illicit purposes, assuming that all aren't.

Sure it is. Try extending this argument to every other kind of business. Most shops, for example, don’t let you take whatever you want off the shelves and promise to mail them a check later. Even if many people would be honest, enough wouldn’t that it would make their business unsustainable (or at least substantially less profitable). Therefore, they almost universally prohibit this.

That’s just one example among many. The logical conclusion of your argument is that it’s unacceptable for any business not to extend unlimited trust to all their customers unconditionally.

Why is it not acceptable if a machine is not being used for its intended purposes and most people using it are for pirating games?

Why is there any notion of acceptability for a company’s rulings on how their copyrights should be protected?

One might say that you bought a license to a game. And that license includes only being run from the physical copy you received. Nintendo is only getting worse with this over time. Just see for example the Breath of the Wild DLC... No physical copy to be obtained, forever bound to your nintendo account.