Highly unlikely. That would require designing a new spacecraft from the ground up while also developing new robotics and operations technologies. I'd peg that mission at $300 - $500 million. NASA would almost certainty be better off documenting lessons learned and pursuing a new observatory.
I think part of the reason the JWST took so long to build was the complexity of the design. As in, it was difficult to manufacture and assemble and test due to the way it was designed. It might be cheaper to do it a second time based on the lessons (avoiding mistakes) from the first, but it would probably still be quite expensive.
I wondered the same thing. I once read this commentary on project management (disguised as a StarWars fanfic)[1] which makes me pessimistic. However I'm in no way involved so I'd be curious to hear what someone more knowledgable thinks.
That 0.5 billion (which to be clear, is a number I made up) won't guarantee that JWST will be fixed. The "fixer" spacecraft could end up failing itself. Or it could discover new problems that it's not equipped to handle.
Also, congress would be extremely critical of NASA if JWST fails. They would not be excited to shell out another $0.5 billion for a chance to fix it.
Not to mention that we don't even currently have a real capability to repair the currently malfunctioning Hubble telescope anymore. That was designed for maintenence from the now non-existent space shuttle in mind. Trying to accomplish the same with the Dragon would be unknown territory and it seems that there is little desire from both NASA and congress to even bother.
JWST in comparison is a far trickier and complicated beast to tinker with. This is the biggest reason why they are so paranoid about any fault before orbital launch. It would be all but impossible to service it - on both a technical and political level.
