In France (~75% nuclear electricity ) they do, using Westinghouse-style Pressurized Water Reactors (PWR).
France often has to buy huge amounts of Energy from Germany (regeneratives) during winter and summer. Whenever the weather gets somehow extreme.
So it's not as if those reactors are making a stable energy grid.
Especially with higher and longer high temepratues due to climate change nuclear has a big problem getting cooling water since the rivers can get so warm they can't use any of it.
I don't agree with your statements.
https://www.nsenergybusiness.com/features/electricity-export-france/France exports 9.3% (of French electrical generation).
Germany exports 5.7% (of German electrical generation)
The report suggests Germany was Europe’s second-largest net exporter and was the second biggest market for France’s exports during the period.. (ie Germany is an importer too)
Imports of electricity to France represent 0.5% of demand.
Imports of electricity to Germany represent 1.0 % of demand.
So imports to either Germany or France are local load balancing, not major stuff.
Many French reactors on rivers use air cooling, with minimal water input, and the water temperature is a minor factor. This is make up water for the water lost in evaporative cooling in the cooling towers.
Of course if the water level is too low, you can't get (or are forbidden from getting) that make-up water.
The majority of nuclear plants in France are located away from the coasts and obtain their cooling water from rivers. These plants employ cooling towers to reduce their impact on the environment.
via
https://en.wikipedia.org/wiki/Nuclear_power_in_FranceExceptions to the river water use for direct cooling include Fessenheim (on the Rhine Canal), to German irritation :-)
I looked up the cooling vs source on Wikipedia, and have been to (worked at) Cattenom, Chinon, Belleville, all of which use air cooling (evaporative), and to Fessenheim.
I've also been to Philippsburg (worked there during Unit 1 decommissioning) and Isar (just a visit), both in Germany.
As side note, I live near a reactor in the middle of the desert, it also uses evaporative cooling to air, with some water make-up intake, but no discharges back to the river.
In winter, you can see the condensed vapor, but in summertime at ~40C (104F) at full power no vapor could be seen.