I bet, we will develop that technology in much much shorter time than we need to store nuclear waste.
Again, the only reason we're not all nuclear today is because of politics.
That's probably the wrong choice.
It's a way to drastically reduce the waste from the process.
Understand where reprocessing came from. Way back then, the story was that nuclear was going to be dirt cheap, but would ultimately be limited by the cost of uranium. The solution was breeding, to provide all the expensive fuel those thousands of cheap reactors would need. Reprocessing was needed to close this fuel cycle.
But this story bears no resemblance to reality. Reactors turned out to be expensive, the number of installed reactors was far below projections, and uranium is not in short supply.
One still hears echoes of this old narrative from people who don't really understand where it came from, and why it doesn't apply.
But let's stipulate that they want to destroy the waste. What's the cheapest way to do that? If they wait to reprocess the fuel, and destroy the actinides in the future, it comes out cheaper than if they reprocess now. That's because reprocessing, and developing and building fast reactors, is quite expensive, and the net present value of that cost is minimized by moving it off into the future. Moreover, reprocessing becomes easier as the fuel cools off.
So, reprocessing NOW is a pointless waste of money, even if ultimately you want to do it. The ONLY reason you'd want to reprocess now was if you needed the actinides now for use in energy generation. And no one needs them for that.
The point is to deal with the waste. The whole argument is that we can't go to nuclear power because "waste". So deal with it.
No one cares about the cost of it -- it's far cheaper to deal with it now than to manage it for a thousand years anyway -- especially in political capital with a bunch of nimbys who think nuclear power is scary.