It creates highly toxic waste products that nobody wants to keep stored for centuries in their backyard, just not a lot of CO2. That gets waved away a lot like it isn’t an issue. It’s better than burning gas, oil, or coal. It’s not better than renewables in my opinion. And nuclear needs a reliable cooling chain for its survival and all the people unfortunate enough to live close by. That’s normally done with water that happens to flow by the plant. If the increasing heat dries out these rivers, you’ll get a slightly more stretched out version of Fukushima.
It’s a very small amount that can be contained in secure casks and concentrated in a particular secure location in the middle of nowhere as opposed to other industrial wastes that are blasted out into the environment and our lungs.
You do need cooling water to keep a plant operational at full power by ensuring your condenser can handle all the steam coming in. If it can’t due to declining river volume then the operators must reduce power (thus making less steam which needs less condensing), if they for whatever reason were not paying attention to the alarms going off then their plant would automatically shut down for loss of condenser vacuum and restore that margin by itself. You don’t have to use rivers as the source of cooling for every nuclear reactor either though some existing ones are designed that way. You can source water from oceans, lakes, groundwater, heck you can make artificial bodies of water that are filled with surplus water and can be used in times of diminished water from whatever is used to feed them, etc.