- the nuclear plants require a lot of sweet water for cooling, 24/7, and the world is running out
Not really. Only once-through nuclear plants require large amounts of fresh water continuously. Most plants use cooling towers instead. Some plants don't even use water in the recirculating parts of the cooling systems (e.g. molten salt reactors).
Also, once-through reactors, if designed to do so, can use salt water instead of fresh water.
- it's pretty much unflexible regarding any peaks or lows in consumption
Only because they aren't designed to do so. You can significantly reduce the output of a plant very quickly, but you can't speed it up quickly, currently, because of the buildup of Xenon-135 as a fission byproduct, which is a strong neutron absorber, and the only way to get beyond that is to pull the fuel rods out far more than is safe, and once the uranium fission restarts, the Xenon is quickly destroyed, resulting in a rapid increase in neutron levels in the core, which would overheat the reactor before you could bring it under control.
However, there are a couple of designs that don't suffer from that problem—integral fast reactors and molten fuel reactors both allow the xenon to be separated from the fuel. And I think pebble bed reactors could also be readily made to be largely immune to this effect by cycling in different fuel pellets in while the xenon in the recently used pellets slowly decays.
- the latest generation concrete housings' carbon foorprint takes a decade to offset
I think your numbers are way off. According to David MacKay, spread over a 25-year lifespan, it only comes to about 1.4 grams of CO2 per kWh. In other words, it offsets its construction cost compared with coal in just a little over a month, by my math.