Many historians work on manuscripts and/or large archives of documents that might not be digitized, let alone be accessible in the internet. The proportion of human knowledge that is available in the internet, especially if we further constrain to English-language and non-Darkweb or pirated, is greatly exaggerated. So there are infrastructure problems that LLMs by themselves don't solve.
On the other hand, people tend to be happy with a history that ignores 90+% of what happened, instead focusing on a "central" narrative, which traditionally focussed on maybe 5 Euro-Atlantic great powers, and nowadays somewhat pretends not to.
That being said, I don't like the subjectivist take on historical truth advanced by the article. Maybe it's hard to positively establish facts, but it doesn't mean one cannot negatively establish falsehoods and this matters more in practice, in the end. This feels salient when touching on opinions of Carr's as a Soviet-friendly historian.