Slower to roll out, yes, but the change would have happened long ago so we'd be talking about incremental upgrades anyways, not new construction everywhere.
As far as cost, nuclear has the fewest deaths per unit energy generated (yes, even including renewables) and is only more expensive than fossil-fueled solutions which would be disfavored due to carbon emissions concerns. Renewable can be less expensive (which is why I mentioned it).
The current nuclear cost estimates include some rather insane design margins, containments, redundant system after redundant system which could all probably be reduced a bit without appreciably affecting deaths/TW-hr, which would make it cheaper.
Also, a major portion of the expense is from very restrictive contamination handling requirements to keep radiation exposure to the workers themselves at extremely low levels. These levels could probably also be increased without detectable increase in cancer rate (in fact, it may even reduce cancer incidence; see radiation hormesis). Would we really say that nuclear workers absolutely much be safer than coal plant workers, coal miners, etc.? We do now, and this also makes nuclear more expensive.
Besides, if it's true that there is an undeniable nexus between all civilian nuclear power programs and nuclear weapons programs then it is probably imperative to take much stronger action against Iran than we are currently taking, since we can't trust their assurances that their program is strictly for civilian power generation. Unless of course, we're willing to allow them to further destabilize the whole Middle East region.