The deepest mine in the world is 4km deep. There are only a dozen or so more than 2km deep. Going down 5-6km may be possible, but definitely not with "no issues".
You don't need to drill tunnels for people to walk in - just a borehole wide enough to fit a cylinder filled with nuclear waste.
In fact, this very idea was already researched and test holes drilled - but of course was cancelled due to public opposition, even though we could get rid of our nuclear waste almost overnight using this method. Typical.
As per your Wikipedia article, current technology limits the borehole to 50 cm. That gets us 500 to 1000 m^3 worth of storage per borehole, assuming the lower 1km to 2km is used for storage.
From this[1] page, as far as I understand, on a global scale the current amount of nuclear waste in need of such storage is 482000 m^3. So roughly 500-1000 boreholes to store the current waste inventory.
Anyone got any ideas on how much it costs to drill a 5-6km 50cm hole?
In fact, this very idea was already researched and test holes drilled - but of course was cancelled due to public opposition, even though we could get rid of our nuclear waste almost overnight using this method. Typical.
https://en.wikipedia.org/wiki/Deep_borehole_disposal