Google "downwinders" and "upshot knothole project" for details of why Utah is worried about this. And then do a little subsidiary googling on cancer rates in the seven westmost US states as opposed to the Eastern seaboard.
Also google "Washington State" "Hanford nuclear reservation" and "Russian thistle" for other examples of how our government keeps a close eye on its radioactive byproducts. Yes, that's right.
We can definitely trust these guys to built a high-level nuclear storage facility in a leaky mountain 90 miles from Las Vegas, don't you think? Especially when they'll be shipping the waste near your town, too.
ETA: FYI, there are no nuclear power plants in NV. None. All the waste would come from out of state.