There is definitely opposition to nuclear power on moral grounds. There are those who feel it is more moral to lay waste to hundreds of square miles of land, kill hundrreds of thousands of people and displace millions that to use nuclear power. it is more mortal to prop of thugs in more than a few extremely repressive regimes than to use nuclear power. And so on. We won't decide this issue on PF, but we should not deny that it exists nor that it plays an important role in policy and decision making.
How long does nuclear waste last? That's an ill-defined question. Until the last atom has decayed? Until it is less radioactive than medical waste? Until it is less radioactive than the ore it was extracted from? The latter is about 2500 years. However, at this point all the remaining isotopes are long-lived: after half that time, your waste is only slightly more radioactive than the ore, and so on.
In my non-expert opinion, there are really only two isotopes you need to worry about: Cs-137 and Sr-90. Both have half lives around 30 years. So after a century, perhaps 2, there is very little left. At that time, everything with shorter half-lives is gone, and everything with longer half-lives is not all that radioactive.
I would also argue that waste should be reprocessed for medical uses before vitrification or whatever. There is a worldwide shortage of Tc-99m. We should extract the parent Mo-99 as soon as we can.
Note that extracting the remaining unburned fuel makes the waste more radioactive, not less. I think this is positive. You have less volume to dispose of. If you want a higher volume, well, OK, we'll just dissolve it molten glass.