Cut and cover is basically unusable in cities because you'd have to "cut" down all the buildings you'd otherwise tunnel under.

There isn't some industry saying "yes we could cut and cover here, but we prefer the slower more expensive option of a TBM"!

(I see NATM mentioned; there have been safety issues https://www.hse.gov.uk/pubns/natm.htm )

The HS2 cut and cover tunnels were all in greenfield: https://www.hs2.org.uk/building-hs2/tunnels/green-tunnels/ ; much of the cost there goes on planning and documentation, an under-appreciated cost. It's also questionable as to whether they were needed at all; a plain cutting with embankment open to the air would have been fine from a civil engineering point of view, or even in many places just flat track, but the tunnels were planned because people objected to a railway running through fields.