There have been small scale versions of this used in major cities in the past. The primary limitation has been package routing, but that should be a reasonably simple problem now days. Realistically outside major city’s or industrial areas, building tunnels is unlikely to be cost effective. However, in a major metropolitan area it may be cost effective depending on what rates you can charge.
PS: Same day currier companies already use the subway system; they have a "mole" that stays in the subway and hands packages to curriers at each station.
I used to think this is a great idea too, and got all enthusiastic about it. Somehow I changed my mind, no idea why... maybe trying to think about it being cost effective? I'm not completely outside the problem either: a few years ago a co-founded a small courier company, so I did spend some time thinking about how to best move stuff in a big city.
Right now I'd say the right way to go about things is more computing power. A "swarm" of couriers can probably be efficient and cost effective enough. The real break will come when we can have cars that drive themselves, so you don't even have to pay a full time human to move packages around.
But digging holes? In the few instances where you can actually do it, they're great. It's just that I really doubt it's at all scalable.