I think more than 1-2 good breaths per reg is wasting gas- at least as a reg check. It does however ensure you've used enough to note a drop in the SPG if the valve is off. On a technical diving configured regulator with just a single second stage and inflator hose, the system's volume is low enough that 2 breaths will do it, even with a long hose primary.
What I've often seen come across the service bench are exhaust valves that are completely glued shut with salt, scum, etc, often to the point that it takes a hot soak or hot ultrasound dip to free them up. Obviously those octos will still deliver gas, but breathing off them would take an extreme degree of both calm and solid understanding of what was wrong.
From time to time I've also seen objects in octos such as sand, silt, kelp, moss, and now and then a dead critters (small hermit crab and a fish). All of the above will potentially block the lever and prevent adequate gas delivery.
Many divers bash the Air 2, and it has it's faults in some aspects of diving, but my take away on it 28 years ago when i started diving was: "It's important to use the alternate air source on e very dive to ensure it gets used and thoroughly flushed on every dive, to ensure it will continue to work on every dive".
Consequently, I think it's far more important to actually use your back up reg on every dive, rather than just test it with a few breathes at the start of the dive and call it good. For a recreational diver, that's readily accommodated with a long hose primary and bungeed octo, as the primary can be clipped off for a few minutes while the diver switches to the octo, building skill in smooth reg switches as well as using the octo on every dive.