The risk of environmental mess happening would be way to high.
Yes the option of not having to worry about ocean shipping losses would be nice. And reducing the cost for people to move around would be nice.
The risk of getting something where it is should not be would be a major risk.
There was a Popular Mechanics article back in the 1970's I think which explored the idea of a bridge across the Bering Strait.
There is one other problem of putting anything across the Bering Strait. The mid Pacific plate cross there. Imagine trying to engine around that? Or if a major plate shifted and cracked the tunnel open?