> I'd guess the reason for the 800 ft is because the reservoir it'll draw from is near sea level.
I believe Tunnel #3 connects to the Catskill Aqueduct[1], which draws from the Schoharie and Ashokan reservoirs. Both are at least a few hundred feet above sea level (the Ashokan is about 600 feet above, since it was formed by flooding a valley in the Catskills).
But I have no idea why they dug it so deep, given that! Maybe to give themselves an (extremely) ample buffer for any future infrastructure in Manhattan.
The average depth is more like 400 feet.
One diagram I saw indicated 2 different layers of bedrock. I didn't find anything real clear, but it can be that the lower layer is a more suitable material for the tunnel.