I'm not sure I understand the question. As it is now, the vast majority of my transgressions in real life disappear into a memory hole. What makes the internet so special in that regard? You want there to be a permanent digital record of people's mistakes, why? So that those best at hiding their defects can get ahead? Why is that desirable?
And yet the same community that insists the internet act as a permanent, immutable and irrevocable platform for "judging honesty" tends to object when intelligence agencies, law enforcement and employers use their data for just that purpose.
Even if it were the case that one could only judge a person's honesty and accuracy from the "track record" of content published to the web that can be traced to their identity, this assumes that all such content is unbiased and factual, and that any interpretation of that content would also be unbiased and factual, but that isn't true.
The combination of right to be forgotten and GDPR practically mandate that this be the case and, as others have pointed out, in the pre-internet era there would often be no record, unless it had hit the print media. Most criminal offences are expunged (at least in the UK) from your criminal record after a number of years, so why should the internet be allowed to keep a permanent record after your debt to society has been paid?
For sure, although we definitely strayed into moral territory. Even limiting ourselves to authors though, that's a concept whose meaning is radically different nowadays (when it means anyone who can type - including on a touchscreen - and knows how to hit the publish button on Medium/Wordpress/Tumblr or wherever) to what it was in the past, when it meant having to go through at least some amount of gatekeeping at the relevant publication.
Would you really want some sort of naively politicised rant that you wrote as a teen and no longer believe to affect your ability to get a job in your mid-thirties? Would that even be fair? Of course not. Yet that's absolutely realistic in a digital world that forgets nothing and where permanent and total erasure isn't an option.
(To be honest, age isn't particularly a factor here: over a period of a couple of decades anyone's beliefs can change quite substantially, and plenty do. Granted, plenty also don't, but entrenchment is a choice, even if one made passively).
When you write a piece, if you want to delete it so that no one else can read it, it should be your right. Unless of course you're a journalist and you have a duty to integrity or something like that, but I'm talking about people like you and me who might decide one day that they do not like what they wrote anymore.