Even if they do get their quoted 30 second headways and manage to cram 16 people into a car, and they run 20 hours a day like they're claiming, that's only 38,400 trips per day. Realistically it would probably more like a third of that. The Red Line alone averages 250,000 trips per day.
Most modern tunnels built for existing transit systems are built to fit existing rolling stock, so the idea of smaller tunnels gets ruled out early on. In the past, smaller tunnels were used. In fact, one of the most extensive small tunnel transit networks was in Chicago: https://en.m.wikipedia.org/wiki/Chicago_Tunnel_Company
The small-diameter tunnels we're talking about were built with a tunnel shield, which is the hand-operated predecessor to the TBM.
https://en.wikipedia.org/wiki/History_of_the_London_Undergro...
Of that underground, I Elise the majority is the deep tube bored lines (pic, jubilee, bakerloo, central, northern) rather than pretty much just the circle that's cut and cover.
Technically true, it's 45% that's underground, which includes 32km of cut-and-cover lines and 150km of tunnels out of the 402km total.