Just like the first Starship Enterprise is now Jonathan Archer's ship from the Enterprise TV series
Where does it say that?
All we ever hear is that Archer flew a starship Enterprise
. Nothing indicates a dozen skippers before him didn't do the same. Some
sort of a more or less arbitrary division has always existed between the early starships Enterprise
and the currently six that "count" whenever our Federation heroes do the counting.
Once we thought it might be because the earlier starfaring Enterprises
(assumed, now confirmed) weren't called "starships". Now we can't think that. But nothing has changed in practice.
That's not much of a case of "overwriting" anything, just like George Kirk (now there's a name that has survived well enough despite complete lack of canon status) being the XO of the Kelvin
in 2233 doesn't really contradict anything written about him previously and dictates nothing about what he would have been doing in 2232, or 2234 in those universes where he survived 2233.