The Natchez Trace Parkway is a limited-access conventional road, not an expressway by any means. The Chickasaw Turnpike is a controlled-access expressway but it’s undivided (not a dual carriageway). Capitol Expressway is a divided expressway but it has scant access control.
Data consumer use of access_control=* is basically theoretical, while expressway=yes is in actual use by both renderers and routers. In addition to the use cases I’ve already mentioned, any router that handles default speed limits globally must consider expressway=yes in some jurisdictions, because that’s exactly how vague the law is.
So by all means promote tagging specifics such as access control, but they aren’t a replacement for classification.