I feel like there is at least a certain amount of integrity when the laugh track comes from a live studio audience.
Yep. I loathe pre-recorded laugh tracks, but I like live studio audience laughter. It makes a huge difference that people are laughing at what actually
is funny rather than what the show creators
want to be funny. That said, I've been in a live studio audience once, and I vaguely recall some laughter being added in post-production for jokes that fell flat with the live audience.
Red Dwarf is another UK show that used a live studio audience for laughter, though I haven't seen it since I was a kid so I don't know whether I'd like it today.