There are some 25 elective adventure dives you can choose from for AOW, including Enriched Air, Cavern, DPV, Deep, Rebreather, some Project AWARE, etc.
The PADI AOW manual contains materials (course info and knowledge reviews) for 13 of the 25 adventure dives. This set of 13 dives can be done by any open water instructor and do not need the instructor to be certified to teach the full specialty. The other 12 dives, which include Enriched Air, Ice, Cavern, etc. require the instructor to be certified to teach the specialty so it's not included in the manual.
If a shop didn't have an Enriched Air instructor, they wouldn't be able to offer it as an elective, so it would be safer to consistently offer and promote the electives that all instructors could teach and those with course materials available. Also, if not using the AOW course materials, the instructor would have to adapt the specialty course materials and knowledge reviews to deliver to the student for that one elective dive - a little more effort perhaps.
Because you can't get nitrox without a certification, there's no point in taking a nitrox adventure dive when the specialty doesn't even require you to dive. If you need nitrox, just take the full specialty, learn a little, and pick a different elective dive.