A nuclear power plant can't just "keep spinning without a load" - all that energy has to go somewhere! If a nuclear plant is disconnected from the grid (tripped), the nuclear reaction must be stopped (eg: by inserting control rods into the core).
Of course it can, just short the generator coils and you have a free brake. The turbine should then still have resistance and shouldn't overspeed. Or just idk, use it to pump some water in a loop or discharge through some resistors. Getting rid of power isn't that hard if you want to do it. Simplest solution would I suppose be to just have an outside radiator that brings the steam to cooling tower levels of manageability so you can throttle the turbine with just a valve.
The thing is, they don't really want to do it if they can save fuel by shutting down.
You could just keep it spinning nonstop without a load I suppose, but for anything but nuclear it's not gonna be economical.