The existing nuclear plants provide a lot of electricity. They are meant to last for years and years. If you shut them down now, you still have the same nuclear waste in a couple of years from now. So, it is beneficial to generate electricity from nuclear power than to not generate electricity and end up with the same spent rods. Unlike coal, you can stop burning coal and you still have the unburned coal.
Compared to coal or gas fired generators, there is no pollution with nuclear power except for spent nuclear rods. The both coal and nuclear plants heat up water to create steam to propel the generators. But coal releases smoke into the atmosphere and nuclear power doesn't.