We would have known about near meltdowns by now, which probably would have been more common in the early decades of nuclear navy power, considering we know things like how the air force nearly destroyed a huge swath of North Carolina due to an accident involving a nuclear bomb for example.

    do we know how expensive (per unit energy) 
    US Navy reactors are? It doesn't matter how safe 
    they are if they are twice as expensive as 
    renewables (plus storage / power-to-gas).

Renewables (and fusion, although that's arguably a renewable) are obviously the end goal but until they can fill 100% of our energy needs the real cost comparison needs to be "the cost of nuclear" versus "the cost of fossil fuel plus the cost of the damage done by fossil fuels."

renewables make sense if you can prove to me that you can make them reliable like nuclear, but you can't. Someday I suppose a high density, cheap "battery" tech will happen that will make that true, but right now it's simply not true and the Germans are getting ready to find that out this winter, unfortunately via much higher prices via power imported from adjacent countries using dino-fuel and likely blackouts from time to time.

> reliable like nuclear

To be clear, the capacity factor of France's nuclear power stations is "about 70%"[a] (and was "61 percent"[b] in 1988), while recent offshore wind farms manage a "65% capacity factor"[c].

It's also worth noting that there is less parallelism in nuclear reactor designs than in wind farms, so a single mechanical or structural fault (or just the need for regular maintenance and inspection) can take out an entire nuclear reactor, whereas a wind farm can shut down a single turbine without much impact.

So there are certainly differences in the sorts of guarantees that the different types of power station can provide, but I think you need to be a lot more precise about what you mean by "reliable" in order to judge what, if anything, renewables are lacking as an alternative energy source.

[a] https://www.world-nuclear.org/information-library/country-pr...

[b] http://www.fundinguniverse.com/company-histories/electricit%...

[c] https://www.greentechmedia.com/articles/read/worlds-first-fl...

> For a start, do we know how expensive (per unit energy) US Navy reactors are?

Price does not matter. It has to work reliably, not only in calm days of peace, but during times of war. Having a source of power to move the big boats without relying on external supplies is worth the price. There even were experiments to generate jetfuel using nuclear power on carriers, certainly not because it is cheap.

Price does matter though.

Sure, just remember to account for the environmental cost of climate change when evaluating the true cost of gas and coal plants.