In response to @mnalis but overall I think the topic has surfaced several times in this thread and elsewhere:
For example, such distinguishing may allow apps like StreetComplete to ask for
service=*details on allhighway=serviceways which missservice=*tag.
It is true that a tag that basically means that a highway=service road is none of the service=* values used but “just” a very minor road would be handy for the cited purpose. See also the ticket New Quest: What type of service road is this? (#808) in the app’s issue tracker.
However, the introduction of a presumed service=general that catches all other cases except for the ones currently defined means that no other service=* tag value should be added later, as the introduction of another documented value would mean an implicit redefinition of a presumed service=general.
So, I am not saying that such a tag would be a bad idea, but before such a tag is introduced, we should be really sure that there are no other service road categories for which it would make sense to have a value.
See also the mailing list discussion [Tagging] RFC: service=? for all highway=service (service=parking needed, primarily, I think) for a request for comments of a related now inactive proposal.