And it's a fair bet that SpaceX won't be the only option for putting something like Starlink into orbit over time, so SpaceX might as well take their money and keep it from funding other launch competitors (whether they eventually use Blue Origin & Co, or China, or Arianespace / EU).

Would that compel them to launch their competitors' products into space? Seems like they could just say "build your own rockets".

Yes—same way railroads were forced to carry their competitors' freight, at fair rates. (That when US railroad monopolies were acquiring the companies making use of their railways, so that they could kill off those company's competitors and leverage their rail monopolies into new monopolies, in different fields. These are old tricks).

Except railways occupy land that may physically exclude competitors from being able to build their own (mountain passes etc...). No such limitation exists for launching a rocket.

Antitrust isn't solely limited to natural monopolies. (Also most of the time, what you describe wasn't quite the case—there's many places were there's two, useless railways running parallel for each other for stretch, not for any technically useful reason—just an economic cooperation failure. You can call the monopolist's bluff and build a redundant (n+1)th rail line or an (n+1)th orbital launch company—it's just devastatingly expensive).