A different reason the new Varus lore shouldn't have been used on Varus
Varus's new lore will now make him the third duo(/trio) adc in lore, after Quinn and Kindred, who, from a gameplay perspective, will completely fail to deliver on the thematic of a duo(/trio) champion.
Despite having three personalities fighting for control with any one of them in the driver's seat at any given time, Varus does not have any kind of alternate firing modes, stance swaps, "rage" or "super" transformations to distinguish how those personalities actually control Varus.
Outside of this fact, Varus still has a decent and iconic adc kit, he is not on the schedule for a gameplay update and isn't even really on the radar as a priority to be put on that schedule, so it's probably going to stay that way for quite a while.
It's going to be a shame when someone at Riot actually comes up with a good gameplay idea for a champion with multiple entities or personalities and their story can't live up to the gameplay because of all the champions around with a similar story hook that their gameplay didn't live up to.