In many cases they can't be all that far from land, could one set up a way to run wires?
I also wonder about the possibility for some kind of permanent installation in select places, where small amounts of sediment are continually removed (as opposed to large amounts of sediment occasionally removed). Being permanent means you can hook it up to the grid.
Of course running them over some dirt is easier than through possibly moving water, but still.
It’s definitely possible, I don’t have an in depth knowledge of ships connected to shore power with cables, but if the distance isn’t too great, it seems possible.
Raising voltage lowers the ampacity to allow for smaller conductors.
6MW at 7200V is only ~500A, 6MW at 13.8kV is only 250A.
There are massive electric powered hydraulic mining machines that operate connected to power cables.
I like it, very similar to how mules used to pull barges thru canals except with electrical cables and a rail pantograph running on distribution lines next to the canal instead of mules and ropes.