In the skimmer this contact area (if the air contain its 20 % oxygen) is much, much, much, much greater than an area you can create with waves on the surface.
You sure about that ….. and lest it be less than completely obvious, I am not. Does the total surface area of the bubbles in the skimmer exceed that of constantly turning over the various surfaces of a reef system (including the agitation created by the drains)? I've not tried to do the math ….. probably couldn't even if I wanted to. What I did do, some years ago, was to measure my tank with a DO meter with and without the skimmer and there was no material difference (neither during light hours nor dark). Further, since the 'main' purpose of the skimmer is to encourage proteins to adhere to the bubble/water interface, I also wonder how effective those bubbles actually are at diffusing oxygen if they are quickly getting 'gummed up'. I do not therefore find it necessary to rely on my skimmer for oxygenation, thus using recirculated air …. which was my original point. I do appreciate, however, that not all systems may be so designed ….. thus perhaps your point.