British Columbia

The Straight gets over 300m deep in proposed crossing areas, and has hundreds more metres of sediment before hitting bedrock. That depth makes for unprecedented engineering challenges for both tunnels and bridge supports; not necessarily impossible but certainly not financially feasible. A floating bridge in a place with so much wind and waves is similarly unprecented and probably a non-starter due to the shipping traffic.

The BC government has a good overview page about it. They basically suggest that the only thing that has even the slightest chance of working is a submerged floating tunnel, something which has never been attempted.