Re: Placed underground you say ?
"it's disposal that needs sorting out. "
That's the rub. Right now with uranium-fuelled systems we're throwing away at least 80% of the mined metal enriching it to 3% from the natural 0.5% or less(*) and then throwing away 97-98% of the energy content of the fuel at the other end when it's "spent"(**)
It's a bit like picking an entire apple orchard, keeping one tree's worth of apples, making cider with it, drinking one glass and binning the rest.
(*) "Depleted uranium" is favoured by the military as it burns nicely inside tanks, but it's a nasty environmental toxin, worse than lead. It's also an essential component of hydrogen bombs, being what you make the cases of the things out of to get the multi-megaton yield
(**) The military love the used stuff too, extracting plutonium from it to make bombs.
The USA regards the energy expenditure of enriching uranium for the civil nuclear program as a classified military secret, but the power feeds into the facilities where they do it give a clue that it's extremely high. (power feeds into the centrifuges are also the giveaway for Iran's enrichment program)
All this stuff can be "burned down" happily in a LFTR-type reactor, resulting in that 97% output waste becoming less than 1% (the entire waste output of a 900MW nuclear power plant over a 60 year lifespan is enough to fill a single olympic size pool), as well as eating all the "depleted" stuff too.
It's technically possible to make weapons out of LFTR technology, but the various isotopes are so thoroughly mixed up that you'd need a _very_ large set of centrifuges to do it and some of those isotopes are so hot that you don't want to be anywhere near them(***), which should dissuade most terrorists from trying (being dead before they reach the boundary fence is a good persuader) and the power requirements of refining from the fuel are so noticeable that any country trying would be spotted quickly - especially after what India managed to pull with CANDU technology.
(***) Hot as in "fatal radiation dose in seconds"
Uranium tech is a dead end anyway - it's rare, expensive to refine and sources are limited. Thorium is the better long-term solution and as it happens we have megatons of the stuff already mined and ready for the technology. That's why so much effort is being put into making LFTRs commercially viable.