The handling of undefined access tag values is naturally undefined, so data consumers behave differently. Some equate an unrecognized access tag value with yes, such as OSRM’s default driving profile and OSM Carto. Others equate it with no.
For example, this residential road bridge across Hamburg’s Fährbuernfleet is tagged access=disabled bicycle=yes foot=yes. I suppose a car with the appropriate disabled permit would be legally allowed to drive on the bridge, if they can get there first. OSM Carto doesn’t depict anything out of the ordinary:
For reference, compare Yangon’s Kyaung Kone 1st Street (access=disabled) to Kyaung Kone 3rd Street (access=destination) in OSM Carto:
The FOSSGIS car routing profiles for OSRM and Valhalla happily suggest driving across the Fährbuernfleet footbridge, but GraphHopper avoids it:
There’s nothing really stopping us from using a novel access tag to indicate this situation, but it would be obscure enough that we wouldn’t be able to count on data consumers to get it right. Previously, Amazon Logistics got away with tagging access=customers en masse on parking lot aisles because most people don’t normally want or need to use a parking lot as a through route. access=permit was proposed without so much regard for existing data consumer behavior, under the assumption that data consumers are already mishandling the situation anyways. After all, it isn’t very easy to get permit-required cases right: