I don't know about you but for one thing I don't keep my fish in a bag.
I didn't say that I KEEP my fish in a bag. I'm talking about a fish in a transport bag, of course.
I am aware that there is little gaseous exchange between an air bubble and the water, as the bubble ascends, especially with a coarse-bubble airstone. The take-home here is that both filters and airstones can, if they are set up to circulate water well, bring deep water up to the surface, where it then has time to exchange gases with the atmosphere. That said, I agree that if a filter inflow can be set to plunge well into the water, more water will circulate than with most aeration systems, especially if the airstone is not near the bottom of the tank. I keep the water level a bit low in my tanks, so the HOB filter inflow moves more water than if the water was higher. That makes my tanks noisier, but I'm pretty happy with the combination of that plus a deep airstone or two in each tank.
My point about automatic battery-powered air pumps is that we generally don't stock our tanks to their stagnant capacity, but to their mechanized capacity. In other words, most aquariums are holding more fish than they could without water circulation (and filtration). Therefore, fish health can be compromised when that circulation stops. Power outages in my part of the world can last a long time; up to a day or two, so a $20 aeration system seems like cheap emergency preparedness to me, when a bunch of fishes start competing for a dwindling oxygen supply.
Apart from power outages, most fish keepers have seen fish gasping at the surface at times, and have seen the relief that an airstone can bring them. And even when they aren't yet at the point of gasping at the surface, but still need a bit more oxygen, because of ill health or the side effects of certain medications, or simply because of warmer water (the warmer the water, the less dissolved oxygen it can hold), fish health professionals and medication manufacturers recommend aeration to help bring them added oxygen.....they wouldn't prescribe aeration for an ailing fish, if it did nothing but offer decoration, as in your statement: "Airstones and pumps are purely decorational and serve no other purpose."
This topic reminds me of the thing that I miss the most from my first tank (circa 1959). It was a ceramic Tyrannosaurus Rex with an airline inside, and the air bubbles released inside its mouth made it chomp its jaw up and down!

Ah, the good old days, eh?