One note: new cut and cover projects tend to actually use cover and cut: first the walls are built underground (often piledriven), then the top is covered with a concrete plate, then the Earth dug away from below. This minimizes the surface disruption.
I mean, a lot of subway projects are specifically planned to follow a main road simply because cut and cover is cheaper.
First, all utilities have to be mapped out, then any basements shored up.
Then once the cut and cover is in progress, all utilities have to be re-routed, during, then replaced after the tunnel is cut.
Then, the disruption of having major transit ways shut for n weeks.
Lastly, there isnt a machine to do it. The TBM is pretty efficient labour wise.
Deeper tunnels for longer distance transport do not have any of these limitation.
As soon as you don't need to break the surface, the cost drops significantly, and the speed of build, planning and after care increase dramatically.
I wouldn't characterize cut and cover as a mild disruption to car traffic - it's a shorter duration of disruption than tunnel boring, but a block at a time will be completely shut down.
It quickly is cheaper to tunnel than to make plans for each thing you need to work around to cut and cover.