Perhaps they'll use a warped interpretation of copyright law to do it, or maybe something even more draconian like censorship laws with a punishment for publishing banned information.
Could they do it, technically? Not unless they controlled the entire world's networks, including those of countries with competing aims. Would that stop them from trying? As we've seen with the endless attacks on end to end encryption, I'm sure they'd give it a shot.
I genuinely think our society is one of the most censorship-resistant societies in history. This comes with its own problems (how do you deal with media that genuinely is harmful, like calls to violence or plots to abuse children?) but I think this is the tradeoff that one has to make when dealing with censorship and liberty. The more you make it difficult for the authorities to shut down good speech, the more difficult it becomes to protect against harmful speech.
With online-only records any hard copies will be incidental. The source-of-truth for any record has always been online, and can be retroactively edited with much less fanfare. Incidentally, it will also be much easier to flood the world with the updated narrative.
Hell, we have Musk publicly advocating to edit old online material to suit the new, "more desirable" narrative.
Is it? I feel it's the other way around. For example, just 10 years ago, there were no apps that forbid me from taking screenshots. Copying CDs and DVDs was comparably easy, even for normal folks. How do I copy a Netflix episode again?
Also, you said "On the other hand, it is now easier than ever to make copies of materials that we see." - now you seem to be talking about finding a copy. But those are two very different things.
I would argue that the opposite is true: it is now harder than ever to change the historical record, which is why we now talk about hypernormality and post-truth, where even if there is evidence for something, people will still lie and claim the opposite and be believed. We live with an abundance of evidence, and yet the Orwellian ability for people in charge to tell you one thing one day, and another thing the next, has never been stronger.
And I think you're again making the mistake of thinking of the printing press as a device for printing books or other materials designed to be long-lasting and valuable. In practice, the printing press brought about a revolution of flyers and pamphlets - ephemeral documents that were distributed one day and then abandoned the next. These things should change freely, and many never entered the historical record at all.