I think 25 million USD is too optimistic, since the Starship upper stage has six raptor engines, and the Falcon 9 upper stage has only one Merlin engine, but a launch price of around 60 million US dollars.
But NASA would pay much more than that if it means they can launch a telescope with a big mirror that doesn't need to be folded in. The main problem I see is that they would likely also have to pay for the
entire development of the new upper stage, which would be much higher than the pure launch cost. Since NASA already has JWST, I'm not sure they have much interest in a big new space telescope currently. Other than that, it's not clear what a super large payload fairing would be required for.
> The main problem I see is that they would likely also have to pay for the entire development of the new upper stage
I don't see why they'd need to do a full 2nd stage.
I'm sure a limited run fairing (especially a complicated one like a hammerhead) will be expensive - certainly quite a bit more than the $5 million per unit cost of the Falcon fairings. But ultimately a fairing just isn't that complicated, and SpaceX has a lot of experience with them.
Well, the aerodynamics are different and the launch abort system would probably have to be somewhat different too. The structural integrity could also be quite different. Of course it won't be a completely new upper stage, as it is just a modification, but a few test launches are probably required.
But NASA would pay much more than that if it means they can launch a telescope with a big mirror that doesn't need to be folded in. The main problem I see is that they would likely also have to pay for the entire development of the new upper stage, which would be much higher than the pure launch cost. Since NASA already has JWST, I'm not sure they have much interest in a big new space telescope currently. Other than that, it's not clear what a super large payload fairing would be required for.