And there are already active civilian nuclear propulsion vessels, mostly russian: half a dozen icebreakers and the icebreaker cargo ship Sevmorput.

A variant of the concept is the floating power plant Akademik Lomonosov, a barge housing 2x35MWe reactors. Though somewhat oddly it's not intended as a mobile power plant, it replaces a "normal" power plant being shut down in a far eastern autonomous district.