The only thing Starship might do is bring down launch costs, but you're still talking about billions of dollars here.
For something like James Webb, probably. But that's because we're so used to the "we can only afford one so over-engineer it" approach.
Starship launches should be cheap. And it can put a lot of stuff in orbit. So take the starlink approach instead of the Webb approach. Every university and college - and even community college - will be able to afford to put a small telescope in orbit that will last a year or two before the orbit degrades and it burns up in the atmosphere. Don't try to overengineer these things. Make them cheap and just launch another every few years.
For something like James Webb, Starship is large enough that it wouldn't have had to bother with that fancy mirror-origami engineering. It could have been launched as a single mirror instead. That would have greatly simplified the engineering involved. Starship is so big that the entire mass of the International Space Station would have only taken two launches to create. It's really going to be game-changing.