> This is the exact sort of thing anti-monopoly laws are intended to work against: that a major market force in one market uses that power to intrude or support itself in another market.

That's actually not true. There's some case law about that sort of thing (the Microsoft antitrust case being the most famous), but the basis for anti trust law has always been about price efficiency, not protection of competition for competition's sake (c.f. the Microsoft breakup was overturned), nor consumer benefit.