Unless you want to socialize the costs while you privatize the gains the cost for those 10.000 (in some cases 100.000) years has to be paid for in advance — unless we are just closing your our and expect future generations will happily do that.
Now I don't say there isn't a scenario (irreversible climate change?) where doing precisely that could make sense — what I say is that no fan of nuclear power managed to explain that part to me in a way that convinced me yet. I want more than a "trust me bro" or handwaving optimism.