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They don't release that much as steam, though.
The majority of water discharged from nuclear plants is cooling water, which stays in liquid form the whole way. It's just rather warmer on the way out than in.
I went looking for some number for fun. (Every work day needs a good distraction, right?)
The nuclear plant that provides some of my electricity supposedly intakes 24 million gallons of water per day. As far as I can tell, that is entirely to make up for cooling water that is released as steam. There is a lot more cooling water present in the system which is recaptured and reused.
24M gallons/day = 16,667 gallons/minute. That's a significant amount of water. However, it's several orders of magnitude less than the flow through the smaller hydro power dams in my area. A few that I looked at have average turbine discharges in the ballpark of 6,000,000 gallons/min.
So for the cost (and vast regulatory headaches) of adding a secondary generation unit onto a nuclear cooling tower, you can just dam a nearby river and get 360x the energy.
Edit: I was way off on that 24M gallon/day number. After more reading, it looks like only around 2% of that water becomes steam leaving the cooling towers. So condensing the steam would give us a flow rate of 333 gallons/min of liquid water. That's barely enough flow to operate a water slide at a theme park, let alone generate significant electricity through a turbine.
They are not evaporating 24M gallons a day. Most of that will be returned to the body of water it is pulled from but a few degrees warmer. There's strict limits on how much the plant can warm a river or lake because of concerns about killing fish so plants will have cooling towers in parallel.
That makes a lot more sense. I thought the number seemed huge, but everything I could find said they have closed-loop cooling at this particular facility.
More importantly, if water is in steam form it still has pressure (and therefore energy).
Nuclear power plants are designed to cool down (aka capture) as much energy as possible before releasing the water back into the wild.