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10,000 years may be forever but it's a rounding error compared to the "half-life" of lead that other power plants produce.

No, forever isn't a rounding error compared to forever. No human civilization has any reason whatsoever to make any distinction between "this field over here will be safe for farming in 10,000 years" and "this field over here will never be safe for farming".

In addition, nuclear isn't competing against coal, it's competing against solar.

If anything is competing against solar, it's solar + batteries + high cost semiconductor switch yards + massive amounts of new transmission lines + replacing the panels every 20 - 30 years + being dependent on China for solar panels.

Even simply finding some adequate way to warn is a challenge: https://en.wikipedia.org/wiki/Long-term_nuclear_waste_warnin...

The Great Pyramid of Giza is about half that years old.

Pop all the waste in stainless steel casts huge pile in a geologically stable desert.