I think that it'd be pretty easy to generate parser code in other languages besides C, but it would be a lot of work to do to port the core library itself[1] to those other languages.

[1] https://github.com/tree-sitter/tree-sitter/tree/master/lib/s...

I agree about the Objective-C grammar! Although it looks like somebody's started work on it:

https://github.com/merico-dev/tree-sitter-objc