Powering a single 1000 MW(e) LWR reactor with sea water uranium would require an adsorber field covering 170 square kilometers of continental shelf. The average power/area would be considerably worse than solar.
Also (from second reference): "The predicted cost to extract uranium from seawater ranged from $610/kg U to $830/kg U." Ouch.
You missed the really funny bit where to reduce costs to a "mere" ~$400/kg you attach the sea mining equipment to supply 5MW to an offshore wind turbine which in 2022 will produce around 10MW net. Then it produces enough vanadium to add about 1hr or storage in flow batteries for the wind turbine each year.
It also requires a constant supply of polymer that caps the EROI around 10.
Also (from second reference): "The predicted cost to extract uranium from seawater ranged from $610/kg U to $830/kg U." Ouch.