It should be noted that these regulations are there to protect the rivers from overheating, the nuclear power plant doesn't really care that much.

They're still a liability though, not only for the reason of heating up rivers

Probably cost. Way cheaper to simply intake and output water than too build and maintain a ground loop heat exchange.

I don't see how that could work. Water cooling is just so much more effective.

A 1 GW reactor operating at 35% thermal efficiency is dumping out 650 MW 2 GW of heat (Edit when I realized the nameplate capacity of a reactor is its electrical output, not its total power). It's hard to see how you can put that heat somewhere in the ground at a continuous rate and maintain some kind of equilibrium.

Evaporative cooling can handle roughly 2400 joules/g of water evaporated, so 1 MW (1 MJ/s) of heat could translate into about 416 g of water evaporated each second. That's what those cooling towers are doing in the stereotypical image of a nuclear power plant.

Meanwhile, if you're allowed to dump the waste heat by discharging warmer water than you take in, water can take on 4.184 J / °C g, so 1 MW would raise the temperature of about 240 kg of water by °C per second.

That's a lot of water used to cool these plants, but there's really nothing that can compete with water at these scales. That's why these plants are next to plentiful water, like on riverbanks next to rivers that have 100-10,000 cubic meters of water per second flowing by. Evaporate just 1 cubic meter (1,000 kg) of water per second for cooling 2.4 GW of heat.

Or, even without evaporative cooling, you could dump about 4 MJ of heat into each cubic meter of water that passes by and only raise it by a single 1°C.

So when the rivers are already running hot or with low water levels, there's really nothing else a power plant could do to expel/reject all the heat it's generating.