Your comments

I agree that pressing Cmd + Shift + P should close it again, the same as pressing Cmd + F twice will open and then close the Find menu and Cmd + R twice will open and then close the symbol menu.

The UI should be more consistent.

I hope someone develops this - unfortunately I'm not a programmer and only work with javascript / css, otherwise I would give it a go. I'll keep an eye out :-).
I really disagree that this should be in plugin land. It makes sense to highlight all opening and closing tags / brackets / braces / parenthesis or whatever else.

Whilst brackets trip up my code far more than divs, it feels like an incomplete feature to leave out tags. Other programs like NotePad++ have this feature (screenshot below). I can't see the argument for not having it.