My understanding is that the bubbles in the water column does minimal to aerate the water. The majority of the aeration comes from the bubbles popping on the surface and causing surface disturbance.
I share an observation, but I am not sure how many could reproduce a similar finding in their tanks.
My tank has a pretty high surface agitation, a spray bar directed slightly up and ripples all over the surface. So I would assume a perfectly clear water surface, with optimal flow enabling gas exchange.
My LED lighting is just 2 cm above the water surface, but what I describe can probably be replicated with a focused torch light that shines from top towards bottom. When I look at night, in a dark room from below the water surface to where the LED beams hit the water (or the torch light, if you prefer), I see dust particles and some other stuff (a thin organic film?) that appears almost stationary, even though my spray bar makes me believe there is flow of water everywhere. Ripples on the surface could be misleading, because even water with a layer on top can show some waves and ripples, even though the layer is stationary in the horizontal directions. So the ripple does not necessarily mean flow, or a clean water surface, and could lead us to the wrong assumptions regarding gas exchange.
Inspired by this thread, I tried to convince myself that an air pump may be a nice new toy, but from the calculations I posted earlier, plus the detailed observation of my tanks surface in a spot light, I believe that my old EHEIM skimmer is the better choice to optimise the gas exchange via the tanks water surface. When the skimmer goes on, what I observed disappears. Obviously, as
@Pepere mentions, bubbles breaking the surface could also bring water in more direct contact to ambient air and promote gas exchange.
I would be excited to hear if my observation with a torch light in a dark tank can be seen by others as well. It could be a good clue that we may need to pay a bit more attention to the tanks water surface cleanliness, not just flow or 'agitation', and/or that our assumptions on gas exchange (incl CO2) may not always be correct.
If my observations can't be replicated, then I wish I hadn't posted the above, as it would be a distraction or risks the creation of a new myth.