This doesn't require your record being kept forever, though. You're already dead or guilty.
> the solution here is to educate HR departments to only use relevant criteria when assessing candidates
This won't work. You don't decide what's relevant.
IN ADDITION to removal attempts, we SHOULD ALSO influence (regulation, societal pressure, etc) how HR/etc departments use data they find online about a person.
However, we should use the justice system to deliver the right punishment instead of condemning people to an extrajudicial, de facto life sentence in all cases. The US is too liberal with making information public, while in most countries it's almost impossible to know who had a DUI in the past.
Any cop can arrest you for DUI, with or without evidence. You get a mugshot, a public record, and a booking charge of "DUI".
Whether you get immediately released with charges dropped, or have to fight it in court and are later declared innocent or have the charges dropped, that initial public record and mugshot next to the words "DUI" now lives forever in various public archives.
I have some sympathy for anyone discriminated against for something they did long ago but the solution here is to educate HR departments to only use relevant criteria when assessing candidates. Or, in other words, reset the social contract a little.
[0] Bonus rant: this fact is why I've always been consistently vocal that the people trying to put so much liability on self-driving vehicle operators that it'll slow down deployment need to take a long hard look at themselves. We need to get humans away from the wheel ASAP and if a couple of people die on the way there those are lives better spent than what we do now.