Because you can generate power without adding CO2 to the air, or other pollutants. It works 24/7/365 and it requires no new "science" to produce.
However, the root of your question appears to me to be founded in some misconceptions you have about nuclear power. It isn't uncommon because the information in most popular press articles about nuclear power is over 50 years old.
To put that in perspective, imagine arguing the utility of an electric car when your data point is gas at 30 cents a gallon (the price in 1965[1])?
But to talk about nuclear power with current data about how you would design a power plant (and these are the new designs we're talking about), the risks of them leaking any radioactivity, and the risk to people should that radio activity leak and it makes our decision to keep building fossil fuel plants look pretty stupid. It really does turn the whole question on its head.
Nuclear is demonstrably cleaner, safer, lower risk, and potentially lower cost (although how do you price the cost of destroying the planet right?) than any other baseload technology. It even surpasses hydroelectric in terms of externalized costs of habitat destruction.
But I recognize that if you base your analysis on an idea that any new nuclear plant would be identical to the ones at Fukishima (built in 1967) or Chernoybl (built in 1972) it does seem odd that we would want more of that.
[1] https://www.energy.gov/eere/vehicles/fact-888-august-31-2015...