If civilization remains on an upward trajectory of technological development, or even stays flat, we will continue to understand the risks of radioactive waste. We won't go poking through waste disposal sites for no good reason. Barring a major collapse, we are unlikely to forget about them, either - we will either reprocess the waste down the road when breeder tech catches up, or we'll continue to make risk-appropriate investments in maintaining the perimeter fence and keeping the sites secure. Now, one could argue that 10 millennia of site maintenance is an expensive endeavor to foist upon our descendants, but that's a different discussion.
The only scenario where we forget about these sites and the dangers of them is some hypothetical future collapse of civilization, where records are gone and the survivors have regressed to a pre-industrial understanding of the world.
If you're an optimist, you don't expect that scenario to happen. But suppose it could - doesn't it make more sense to invest in carbon-neutral power technology like nuclear and maybe help stave off a potential collapse, rather than worry about a small number of the survivors dying of radiation sickness?