I'm not saying it gives the same as the filter output.
I bet it does. As I said in my post above, each bubble creates additional surface area and agitation as it rises to the surface. The more agitation and available surface oxygen, the more oxygen in the water, right?
You're saying oxygenation comes from agitation of the surface. Yes, that's right. I'm saying that I have a filter, I also have a bubble wand in a location where it doesn't even get seen (which isn't the point, but it shows why it doesn't matter to me), and this also agitates the surface and creates additional water surfaces (the outside of bubbles) and agitation. It would be nice to do a scientific test, but I honestly believe that if you have a fish from a river with high oxygen, you should have as much oxygen in your simulated river as possible. I think I have more oxygen with filter + bubbles than I would have with just the filter.
As I said above, I also use it to create a flow in my tank. We cannot lose sight of the fact that we are creating a simulated river (unless you have lake fish, obviously) and we can in no way replicate their natural environment, it is simply not possible - ever - no matter how big your tank, no matter how much you might dislike one of the things you put in the tank.
The basic point I want to make is, I'm doing what I think is best for the fish, not the aesthetics of my tank. Your point about never having seen bubbles in a river actually made me laugh because I'm pretty sure I haven't seen a heater, either. That's all I'm saying...