It is true that in the immediate aftermath of Hastings, life for most folks continued on largely as it had before.

But in the longer term both the administrative structure of the country (which very much affected individual folks' lives) and the language were significantly changed.

I don't see a reason to privilege one of these over the other. You could make the case, for example, that WWII was of little consequence because Germans today live much the same sort of life that they'd have been living if there had been no WWII. That's not clearly a false claim about people's lives, but it doesn't really serve the purpose of understanding the consequences of war very well.