Nukes require lots of cooling, needing access to large amounts of water from water bodies, that's definitely not "most places" by definition.
Two units cooling for every unit of electricity, at least with PWR/BWR. At a 10 degree C rise it requires about 50ml of water (per second) per kW of electrical power.
Palo Verde NPP in Arizona happens to be in a rather dry area. It uses treated sewage for cooling and is trying to use rather poor quality groundwater too.
https://cronkitenews.azpbs.org/2020/02/25/palo-verde-nuclear...
This limits a lot nuclear facilities placement.
Only in rare cases, such as during revisions or emergencies, they might be unable to cool the condenser using the tower-coolant-loop. Then they might have to warm up the water temporarily.
> you definitely don't want to have a nuke potentially discharging contaminated water near population centres (in case something goes wrong and the discharge needs to happen).
There is no such failure case that a "discharge needs to happen" for the irradiated water. There is a comparatively tiny amount of deionized and supercleaned water in the reactor that is always cycled around. Even if such a case were to occur (how??), the amount of water would be easy to handle/store.
https://en.wikipedia.org/wiki/Kingston_Fossil_Plant_coal_fly...
And Brits are not exactly leaping into action about raw sewage discharges into rivers.
These are hardly the only viable plant designs that exist. Molten Salt, Pebble Bed, and other designs exist.
China is currently underway building a molten salt cooled Thorium reactor.
Russia also had lead-bismuth reactors, at least militarily, with the Alfa-class.
[0]: https://www.neimagazine.com/news/mox-use-at-russias-bn-800-r...
