Or would it be more effective to iteratively refine access=permit? Despite the wording of the access=permit draft proposal, access=permit is already routinely being used for a variety of permissiveness, anything from “just ask” (some protected areas) to “boarding pass required” (after security at an airport) to “resident permit only” (street parking). It was inevitable given the plain English meaning of the word “permit”. Some of these uses have already been tagged with permit=* or parking:*:permit=* to clarify the intent.
Routers don’t necessarily distinguish between access=private and access=permit in the manner that one might think after reading the relevant wiki pages. Some routers ignore access=private at the beginning and end of a route if doing so would get the user closer to their destination. Valhalla equates access=permit with access=residents, but both behave just like access=yes, which is an oversimplification even in the case where access is routinely granted. (Don’t you still have to ask for the permit? Wouldn’t that potentially require a detour or at least a delay?)