I don't use ligatures, but I really don't see a problem with other people using them. It's fine, it's a style preference thing, that, like fonts and colour schemes, is as much fashion and personal preference as it is anything. But it's fine.
Syntax highlighting without context is not really a good experience. The highlighter needs to know what language you're using, and a pretty good idea of how to parse it.
And the comment on ligatures below points out, this is actually true of ligatures for human languages as well, but I doubt the font engines are properly tuned for that either. I'd make an exception for the 'obvious' ligatures like gg gy etc where the descenders were overlapping without a ligature. That shouldn't be an issue in a monospaced context though.
For example, in C, what highlight category do you give to '*c'? A declaration, a dereference, or a multiplication call?
In Lisp, is the first element of a list a macro or a function (or a value)? If there's a reader macro, it gets even harder.
But every classification the highlighter does do must be accurate, or it's a buggy highlighter.
And FWIW, it's certainly possible to write a syntax highlighter that does parse the whole program. You'd normally find this in an IDE rather than a programmer's text editor. For example, writing Swift in Xcode, everything gets precisely highlighted, to the point where references to real types are highlighted whereas references to unknown types (e.g. typos) aren't. It's not practical to do this outside of IDEs, which is why most syntax highlighting only tries to highlight that which it can unambiguously determine.