I’m pretty sure the BBC didn’t think that TC2 and 3 would be block booked for ITV with standing sets for more than a couple of years. I think i read that TC2 wasn’t initially kitted out with its own gallery and that it was to be used (at first at least) as a glorified scene dock. The plan was that the refurbished TC1 and 3 would be available for hire on fast turnaround shows. It made sense for Studioworks to take Itv’s block booking for the short term, but had they known it might be for a mid to long term standing set booking I think they may well have suggested elsewhere.
Yes - the initial TC1-3 plans were really based on the requirements of studio shows made by BBC Productions (most of which is now BBC Studios) - and effectively ignored the large number of Indies who made studio studios for the BBC (and ITV/C4/C5/Sky shows that also used the studios as they were marketed commercially) They retained the studios that they knew 'in house' productions could use effectively, but it felt like they ignored other requirements.
TC1 for the big entertainment shows (Strictly etc.), TC2 for Strictly It Takes Two, Watchdog, Crimewatch etc., TC3 for music and entertainment shows, panel shows, sit com etc.
ITV Daytime moving into TC2 and TC3 has made very sound commercial sense, but it has blown the original justification for keeping just 3 studios slightly out of the water...
And as for the most live output from TV Centre being in this era? I think when BBC World and BBC News 24 were both running continuously from TV Centre, along with Breakfast, Sport from TC5 etc. they were making more live TV on the site.