You're wrong, here's all the details for Hinkley Point C:
https://www.gov.uk/government/publications/hinkley-point-c-f...
EDF have already planned spent fuel storage and decomissioning, and it's provided for in the prices.
That's just one example, but it's been the standard practice across nuclear projects for decades now in most of Europe.
> Unless we can see evidence that the system as a whole (i.e. nuclear industry plus government of various levels of corruption) can function to process and store waste safely, this is a black mark against the nuclear industry.
It is being done today, and there are multiple projects that intend to improve upon it ( by recycling or cold underground permanent storage). What kind of evidence do you need? For it to be done over a 100 years? It'd be far too late then.