If you think about this for a minute, maybe you'll be able to form a theory for why this is already very common for military vessels, but not so much for unarmed civilian ones...

Icebreakers are not military vessels and they have nuclear reactors.

Probably initial cost is the reason this did not become something more common.

I guess this is not exactly "cost", but also lifetime spans. A nuclear reactor can sustain a ship for about 20+ years, and that lifetime is too long for many ships, who would be headed out to the scrap yard in less time than that.

Yes, but they're also not regular old merchant ships by any means. All existing ones see to be operated by a Russian government-owned corporation.

> We need to start fitting nuclear reactors on cargo ships.

That's a great idea, and it's timely too. Right now, cargo ships are being attacked in many parts of the world.