Mastering buoyancy is part of open water for every single agency out there and WRSTC requirements. However, I believe, and I infer this from your statement but do not want to put words in your mouth, that this is not the case most of the time.
Using PADI as an example, as it is the most common case and people refer to it so much, the prequisite for Deep is Adventure Diver, which we all know is 3 adventure dives, the first dive of 3 different con ed specialties. So hypothetically, in the PADI system, a diver is "qualified" to take Deep after 7 dives. (I don't have the deep IG guide in front of me, so I am guessing there is no dive count requirement for deep). 5 or 7 dives, not much difference really. Especially if Fish ID or UW naturalist (which are valuable as complete courses by a qualified marine expert) count to that adventure diver rating.
For deep diving though, I fail to see how BLS, O2, and AED are useful for deep diving. Not sure how stress & rescue (the SSI course name for rescue, possibly others, but not PADI).
Again, it depends on an evaluation. With with my OW students in the past who were naturals, I'd still require a fundies like skills course (could be Essentials, fundies, or a NAUI/SDI course where the instructor augments the course to have similar skills requirements) if they were going for the shortest path to deep course that included either a twinset or sidemount (they'd first have to be trained elsewhere) to ensure they are solid divers. I personally require either twinsets or sidemount for anything below 30 meters/100 feet.
None of the boat captains in my area respect the PADI AOW rating. Not one. Hence my prior recommendation for fundies and then deep with an agency other than PADI. Fundies is respected (and preferred).
