It's also going out pretty far (the L2 Lagrange point on the other side of the moon), so they also won't be able to perform any manned post-launch repair missions like they did with Hubble.
In terms of hardware that's readily or soon to be available, it is technically possible. Starship, if it gets off the ground, is the obvious choice. Orion could do it, but it would mean dumping another two billion into JWST.
If it really came down to it, Falcon Heavy launched with a Crew Dragon sitting on top of it could probably reach it, although it might need an additional kick stage (I haven't done the maths), and it would need to be crew rated first (and SpaceX don't currently have an interest in doing that).
Also, AFAIK, Crew Dragon does not have airlocks or other resources for EVAs. Not sure it the capsule can be evacuated for that too. But I would like more information in this issue ... could not find too much from reliable sources for now.
True. But generally when people bring up the statement that we can't service it, they usually back that up by citing the distance. There would still be a lot of hurdles to overcome, but none are insurmountable with relatively small investment.
All of that said, if Starship works, then the economics change drastically anyway. You could probably launch an entire fleet of less reliable, but much cheaper telescopes, for less than the cost of servicing.