Oh, what a tangled web we weave ..... especially when the code panel crosses over into design issues!
OK, as I see it ....
An "SABC" is defined as a 20 amp circuit serving the required receptacles, as well as receptacles serving the counters. If a receptacle is not a required one, and it does not serve the counter ... it need not be on an SABC. (Why do you think they put in the 'refrigerator exception?)
Place a receptacle on the wall, more than 20" high, and not only need it not be on an SABC - it is forbidden to have it on one. (again, look to the 'clock exception') We can also have a lively discussion about receptacles under the counter, but that's for another thread.
My point is that a range hood is too high to plug into an SABC, and we're not allowed 'any other outlets' on an SABC.
Regarding cords and range hoods .... Most hoods I've seen do not come with cords. While I personally have no issues with a properly attached cord, I understand the position that such hoods are intended for hard-wiring only. An inspector that insisted on your adding a cord to such a hood is exceeding his authority, and maybe asking you to violate the 'listing and labeling.'
If you're going to run a dedicated circuit, a 20-amp circuit for a 1-amp fan is a code violation. You can't go over 15. I'd even use a 5-amp breaker. That's for a hard-wired hood. Code has already made the decisions for us regarding cord-connected hoods.
Talk about appliance garages does introduce a few other complications, and IMO deserves its' own thread. Simply put, once there's a garage in place, the remaining 'counter' might not be deep enough to officially count as a 'counter' requiring receptacles ... and, thus, cannot be served by an SABC.