Well, it will be soft. But is that really unacceptable? This is a result of 135/2.0 (trying to match the age of the Rembrandt model
)
Yes, that works well. I've used the same selective-focus technique for that kind of shot: tightly-framed candid portrait, three-quarters profile:

But my initial question wasn't whether it would be possible to find
any application for a 50mm f/1.0 lens on a crop-sensor camera, but rather who would have sufficient use for one to be willing to spend $1500 U.S. for it. And it was a real question, not a rhetorical criticism of Fuji's decision to offer the product. Presumably they didn't design it for the apocryphal dentist with a closet full of unused Leica gear. My brother used to work for Fujifilm and they don't think that way.
Again, assuming the lens is optically good enough to be used wide open—and at that price, it ought to be—the two applications that immediately came to mind were portraiture and low-light shooting (e.g., streets at night). But it strikes me as a suboptimal aperture and focal length, respectively, for those two applications. At normal portrait distances, I think f/1.0 is going to be too shallow for most subjects. And for most low-light situations, at least in my experience, a shorter focal length (34mm or 23mm on a crop sensor) is almost always a better choice.
So what else am I missing? Other than the Rembrandt effect?