Hi, MxxxCon!
Thank you for paying attention to this.
The access=no tag was added based on the fact that it is a correctional facility and doesn’t have public access. According to the OSMwiki, access=permit is used if the access is restricted, but everyone can get the access, so it is more like just a procedure. In this case, it is a correctional facility with strict rules, where not everyone is allowed to get access to the territory, besides, it is necessary to observe a number of rules, including the form of clothing, the availability of documents, which also requires time and preparation. Also the tag already exists on the gate and some of the facility’s roads, and for the map’s accuracy the access=no tag would be preferable.
https://wiki.openstreetmap.org/wiki/Tag:access%3Dpermit
The motor_vehicle=yes tag was deleted for the same reason. According to the Rikers Island Visitor Guide(https://www.libertyfund.nyc/wp-content/uploads/2019/06/2016-Rikers-Island-Visitor-Guide.pdf) and some other sources, to get to the island you need to take a bus and there is no evidence that all motor vehicles are allowed.
We would appreciate hearing your thoughts on this situation and find any potential solutions.

Best regards, Stepan