Liquid / molten salts can be reprocessed "online" and the fission products extracted (yeah, handwaves a LOT of chemistry), so you don't get these partially transmuted solid rods.
Even if you have solid rods or solid pebbles doing the primary power, maybe you can have a secondary on-site molten processor to take care of the waste without it shipping.
One of the annoying aspects of arguing with pro-nuclear people is their blind spot for reprocessing/waste. It just gets shrugged/handwaved away, but to the voting public, having a reactor that produces no waste in the traditional solid fuel sense would be a political boon.
The real issue is that nuclear simply isn't price competitive, it barely beats coal. I would like it to be otherwise.
It would be nice, but the list of reasons which are sufficient to stop it happening is very long.
This is also why mass expansion of reprocessing facilities is completely untenable.