Yes, we also need "only one", except in my country it's basically impossible to go a few kilometers from any spot without hitting a settlement (and if you can do that, your point of origin was probably inside a protected national park). That's probably why we still don't have a storage place despite even having reasonable (even if not perfect) geology for it.
Nuclear waste is a mostly artificial problem considering we've known how to recycle/reuse nuclear waste to the point where it is no longer dangerous. The actual hurdle to nuclear adoption is really more about concerns with nuclear proliferation since a lot of the recycle tech can also be adapted to create weapons grade nuclear fuel.
Additionally, even with no nuclear reactors whatsoever, we'll still have to deal with nuclear waste as it is used in various other areas like medicine. The Goiânia accident incident in Brazil killed many people _immediately_ (unlike Fukushima) and originated from a defunct hospital, not a nuclear power plant. We need to find ways to deal with this stuff regardless if you use nuclear power or not.
> Nuclear waste is a mostly artificial problem considering we've known how to recycle/reuse nuclear waste to the point where it is no longer dangerous.
These repositories are meant specifically for the separated waste from the recycling/reusing process. So the process you're suggesting is the one that creates this "artificial problem".
I had this discussion on HN a while ago and looked into it - the costs of transportation are high because of various logistical regulations, there is a high cost upfront cost to set up a disposal site, there is a fairly significant cost for staffing such sites, and these sites will need to be managed for millennia.