I used to have the DVD of Ripping Yarns which had the option of laughter track on or off for most episodes. Improved some made others worse. Bottom was really good as you could tell Rik Mayall especially was playing to the crowd. However on Fawlty Towers the laughter track which I'm sure was live obscured some of the dialogue and as John Cleese is verbose in it and talks fast the subtitles weren't accurate ir as funny as the actual dialogue and they came in before the punchline, maybe because I'm a fast reader I don't know.
Of course Ripping Yarns was recorded on location so would have been a screening, not Live audience.
You are right about Fawlty Towers, and there are several technical faults too, like boom shadows up the wall especially in the foyer. I have all of them on DVD. I think the thing is, often the big laughs were with stunts (Manuel hit on the head etc) and in any case, as you allude to, Cleese's performance was totally manic and OTT. I should imagine both he and the director decided not to reshoot many such scenes, because they know that doing it again will not get the same, big laugh. That's inevitable. Better to have a messy, technically-flawed scene which is an absolute ripsnorter, than risk doing it again with the laugh not half as good. They may even have reshot such scenes, but then chose the first one at the edit.
Those shows were all about the performance on the night, with that audience, and all the better for it IMO.