I think you're assumption is wrong. As a hardcore freshwater aquarist, tank water oxygen level is of extreme importance. I would say that there is probably very little difference in surface agitation when using a stone or no stone. In theory, the smaller bubbles of the stone create greater surface area for O2 dissolution, but you are right that very little O2 is dissolved from the bubbles, most is from surface agitation.
My thought, and experience (though not scientifically measured), is that a mass of tiny bubbles bursting on the surface creates more oxygen exchange than a couple of large, wavy bubbles. Yes, no stone probably does create more actually agitation of the surface as measured by actual water movement, but in terms of surface area available for oxygen exchange the mass of bubbles should be superior.
I also inject carbon dioxide into my planted aquariums, and within that area there is much experimentation and study done around bubble size and injection method vs. dissolution rate, with the goal being to get 100% of your CO2 to dissolve in the water (as opposed to bubbling away at the surface). The CO2 issue isn't relevant to hydro, I only mention it to say that I have had experience with many inexpensive DIY and store bought methods to dissolve gas in water.
At the end of the day, for the purposes of hydroponics (increasing oxygen to the roots via increasing oxygen in the nut solution) I don't believe that there would be a significant impact on plant growth rate or production if you are using the same air pump with or without an airstone. That being said, I'd love to see someone actually do a pseudo-scientific study and get a definitive answer. Personally, I think there are so many other variables, many of which are tough if not impossible to control, that affect a plants growth and yield that it would be virtually impossible even for the most advanced hydro gardener to come up with a definitive answer outside of a laboratory setting.
Personally, I have a fairly shallow reservoir and use an old, 6 inch aquarium airstone that I had laying around. I chose that one simply because it was laying around and not of much use for me in my aquariums. Had that not been available, I probably would have used a standard aquarium airstone. For the curious, there are dozens of types of airstones of various sizes and various bubble production sizes.
Now the confession - this is my first hydro grow. I've been a soil grower for years and have really dug into the science of hydro. But, although my hydro experience doesn't qualify me to speak to the results of nut aeration, I think my freshwater aquatics experience certainly might lend some insight into how to get oxygen into a liquid reservoir.
