LSP is an example of utterly horrid technical design.
Stop letting Microsoft design protocols and APIs. They are so. bad. at. it.
Unfortunately nobody else stepped up to do it.
I'm glad that the code editors out there didn't wait for your theoretical better designed protocol and decided to adopt LSP. Otherwise we'd still have editor that only support one language properly, and the rest is treated like text. If the price to pay is that it sucks for the handful of people who have to work with it, so be it. For every LSP developer that suffers there are tens of thousands of downstream users who benefit from better language support in their favorite editor!
Once you get past that, JSON-over-TCP is just another kind of asynchronous RPC mechanism, one that has the advantage that you can build it in just about any language with out-of-the-box tools. Trying to make a plugin system or a COM or CORBA or OLE based system really cuts out the ability to build language servers in most languages, because you have to be able to build the code in just the right way.
In no way does this mean LSP is a perfect solution, but anything synchronous would be a step backwards.
A synchronous function can also have obsolete indexing information if it races with the code updates.
So the LSP crashes and/or goes into a runaway memory consumption loop. And your main application dies with it.
Or what if you want, you know, to be able to use the same LSP from TWO different applications at the same time?
Never mind issues with other managed runtimes not expecting to deal with something else in their address space.
However, to come back to your point, there are much better high performance OS IPC mechanisms for inter process communication than sending JSON down through a TCP wire.
As others point out, Electron.
There are some arguments that do carry water in favor of using a client/server protocol transmitting JSON, in particular, the ability for a nearly complete decoupling of analysis of code and the displaying and editing of that code. Also, LSP was (to my knowledge) the first language/platform/usecase agnostic protocol intended for use in code editors.
I get why this is where a big chunk of developers have ended up, but I do bemoan the lost potential for a language to grab mindshare and popularity on the usability and performance of its tooling and developer experience via-a-vis a custom designed and hyper specific code editor. I mean, Rust and Elm received endless praise for their error messages as a massive boon to developer experience, so it is a facet of language design and implementation that can act as great advertisement. I just hate that the prevalence of LSP at this point precludes custom editors as a first choice in the current zeitgeist.