I don't know about you, but I do not want to block on every keystroke. Program analysis can take time, asynchronous feedback is a natural fit. None of the features I use from LSP should be synchronous.

I can almost guarantee you that a synchronous API would yield a much more complicated design just because many operations can not be expected to reliably work within a few milliseconds.

You want to rename something across multiple files? Well now you add file system overhead and blow straight past reliable frame timings. Good luck waiting for that operation to finish. Of course you could make the API beginRename, and queryRename, or whatever you fancy to see if the operation was successful, but now you're back to what you wanted to avoid: an asynchronous API. Do mind that the example is actually one of the better cases, as many things you might want to do with a codebase are actually more expensive. You will feel the hiccups from waiting in the UI thread and you will loathe the program for it.