> Well I mean, one of the new submarines cost something like $2 billion. The reactor can’t be more than a 20% of the total cost.
Wikipedia claims the latest generation US attack submarines come in at $2.8 billion each. If the reactor is 20%, and the entire propulsion system 30% (to make a comparison to a power plant), shaft power is 30 MW, we get $28000/kW. For comparison, civilian nuclear power plant capital cost is around $1500-$6000/kW, depending on where it's built, the cost of capital etc.
So yes, not 100 times more expensive than civilian power, but still way too expensive to be economically viable. (And to be pedantic, I didn't say it was 100 times more expensive either, just that the advantage of nuclear propulsion for submarines are so great that navies are prepared to pay whatever it costs (and cost minimization is certainly not such a high priority for sub reactors as for civilian ones))
> And permission to use the higher enrichment uranium.
No. Just no. Look, I'm a huge proponent of civilian nuclear power, but HEU for civilian use flies in the face of decades of non-proliferation work (see e.g. the US RERTR program which has been running since 1978). And for good reasons too; given access to high grade HEU, even a relatively unsophisticated actor (such as a decently funded terrorist group) could make a gun-type nuclear weapon. In contrast, an implosion device using Pu is significantly more challenging, and is probably out of reach for non-state actors.
In fact, there is pressure to direct the US Navy to switch to LEU (that is, less than 20% enrichment), precisely for non-proliferation reasons. For example, French submarines run on 7% enriched fuel, and they refuel every 10 years. So with 20% fuel, US submarines could probably make do with a single mid-life refueling.
See e.g. http://fissilematerials.org/library/rr15.pdf for a report detailing various efforts to get rid of non-weapon uses of HEU worldwide.