Probably impractical. Digging underwater is much harder than carefully lowering something on the floor.

They have a handy tool for it.

https://en.wikipedia.org/wiki/Pipe-and-cable-laying_plough

There's already underwater powered trenching/laying equipment they use to bury the cables within X miles from the shore. The Baltic Sea is probably shallow enough to bury it all the way across at a higher cost per mile of course.

Plus it could cause damage to environmental ecosystems.

The C-Lion1 cable that was cut was reported buried 1 meter below the seabed.

Unfortunately, that wasn't deep enough since heavy ship anchors which can dig in deeper than that.