are these space programs really profitable for the billionaires in question? i was under the impression that they were sinking their time and money into them too, as more of a hobby than a money-maker
They aren't. We have currently two billionaire hobby space programs. One is a pure hobby and doesn't do actual space yet (suborbital hops != orbit). The other one exists solely to open Mars for regular access and eventual colonization, in the process also opening up near-Earth space for general exploration and exploitation. If it succeeds, it'll create an unprecedented amount of lasting value for humanity in general.
Really, complaining about billionaire space is one of the dumbest part of the current zeitgeist.
> largely redistributing wealth from the commons to rich billionaires
Which means that you are saying that Musk is getting taxpayer money from SpaceX. This clearly isn't the case, he's sinking his own money into it too
Well, yes, they're a real company providing real services and getting paid in exchange.
Anyway, whether the contracts are private or government is off-topic (if it was, I'd point out that the government is getting a really good deal here, which is a very rare case in large-scale government spending). The point is, all that money isn't being funneled to line Musk's pockets, it's being reinvested straight into "let's go to Mars" R&D program.
The other company I reference have not made a commercially viable rocket that will get you into orbit.
On top of that is that the billionaires are using their money to fly to space, instead of really changing the world for better, which they clearly good do. At the same time there is a significant portion of our community that idiolises these people and acts as if they are in fact changing the world for better.