But they do have constant height in the sense that, unless you resize the window horizontally, the height doesn’t change.

For what it’s worth, modern browsers can render absurdly large plain HTML+CSS documents fairly well except perhaps for a slow initial load as long as the contents are boring enough. Chat messages are pretty boring.

I have a diagnostic webpage that is a few million lines long. I could get fancy and optimize it, but it more or less just works, even on mobile.