Admittedly, Tree-sitter has the opportunity to centralize some of the work in incremental parsing that LSP pushes to individual language tooling, but arguably in the modern world of watch-based programming most language tooling is going to feel a need to build it regardless.
The maintenance headache, though, is that Tree-sitter has its own custom grammar DSL, which likely won't look anything like or share anything with the native grammars of the languages it is parsing, and which ultimately has to settle for a lowest-common denominator approach to grammar parsing. Even if it is more sophisticated than so-called "crude" RegEx-based syntax highlighters, it can still at best be a separately maintained emulation of a language's grammar versus the LSP encouraging a language to provide its own intelligence presumably from the very same parser it uses to get work done.
[1] https://docs.microsoft.com/en-us/visualstudio/extensibility/...