The Kelvin Films come out once every 100 years. It's not on anyone's radar anymore. "But they're making Star Trek 4!" Wake me up when they start filming. The normies have all moved on, and so have most people like us.SNW has Enterprise. The Kelvin films have Enterprise.
I can't see her getting Enterprise. It risks oversaturation.
I think if fans can't tell a "TOS" Enterprise from a "TNG" Enterprise, that's on them, not Picard.
EDITED TO ADD: I think the Kelvin Films stalling out and going nowhere was one of the factors that Paramount considered when greenlighting Strange New Worlds.