Yes, it is a problem that one cannot necessarily predict whether a highway=service service=alley is physically passable in a full-width vehicle using that tag alone. A similar problem contributed to the eventual shift to tagging golf cart paths as highway=path instead of highway=service. One reason we were able to make that change was that the practical considerations were already overshadowed by a semantic issue: in plain English, a cart path is considered a kind of path rather than a road. Someone who has never seen a golf course before might mistake a grand cart path for a substandard road, but anyone who is passingly familiar with how these things are used in general would find it strange to classify it as a road.
Introducing highway=alleyway is not necessarily a bad idea, but the question is whether the trouble is worth the eventual benefit. Will anything that the local culture considers to be an “alley” or “alleyway” qualify for this tag too? Then we will have solved nothing despite cajoling mappers and software developers to go along with the change. Or will I need a measuring tape and a list of qualifying vehicle models to determine whether the alley qualifies as a New Alley™? I’m pretty sure that will end up like too many pages on the wiki, a work of fiction.
I don’t mean to say that these tags are totally relativistic. I continue to have to fix all manner of service roads in the U.S. that unaware mappers have mistagged as service=driveway because the local dialect calls most service roads “driveways”, contradicting both British English and the needs of data consumers. Just promise me you won’t take inspiration from driveway2. 