I'm not 100% sure why it's that deep (and can't seem to find a solid explanation). What I can glean suggests that it's partly due to wanting it to be in more geologically stable bedrock that passes below any bodies of water and geological aberrations in the area. And partly so that it can be fed by gravity along a continual downwards slope, which causes it to be fairly deep by the end (then at the end the tunnel narrows, increasing pressure sufficiently to push water up a vertical shaft to the surface distribution network).
"[New York City Water Tunnel No. 3] was authorized in 1954. A third tunnel was needed so tunnel one and tunnel two could be closed for repairs. Stage One was begun in 1970 and completed in 1993 and put into service in 1998."[1]
This seems to imply that the later stages of the old two tunnels have never seen repairs.