The issue of surface agitation and water movement in planted tanks can be daunting. One can read authors that advocate none to those that insist on some, and both sides saying for much the same reasons.
Some surface disturbance likely won't have much effect on the plants. However, we are talking natural or low-tech setups here. A high-tech planted tank with diffused CO2 is a different thing. My comments will be with respect to low-tech, meaning no artificial CO2 addition.
For years, all planted tank writers advocated no excessive surface disturbance (airstones, bubblers, surface movement) because it drove off CO2. A couple years ago, some writers changed, and began advocating the opposite. I was part of an extensive exchange of data on this issue on one of the specialist plant forums with people like Tom Barr. To date, there are no accurate scientific studies to prove this new viewpoint, so any benefit is not assured. There is plenty of evidence to prove that CO2 is driven off faster. This is important because the dissolved CO2 in the aquarium has to be higher per volume than in the air in order to provide sufficient carbon for the plants. CO2 is produced by respiration of fish, plants and bacteria as others mentioned; but the greatest source is in the substrate, from the decomposition of organics. In my humble view, nothing should be done to quicken the loss of this CO2.
Some may have heard of the "siesta" method to discourage algae. The principle is that the tank lights are on for say 5 hours, then off for 3-4 hours, then on again for 5 hours. Leaving aside issues this can cause for the fish, the reason it works to prevent algae is due to the CO2, not the light. CO2 is constantly being produced, but in bright light and assuming other nutrients are present at sufficient levels for the specific plants, the CO2 is usually the first nutrient to become exhausted. Algae then has an advantage. But the mid period of lights off allows the CO2 to rebuild, so when the lights then come on again the plants can merrily start photosynthesizing because CO2 is higher. It is possible however to find a good balance without resorting to this method. My tanks currently have 8 hours daily of tank light, and this is working for the level of nutrients I provide, the natural CO2, and the moderate light, and the plant species' needs; plants are thriving, and algae is present but not troublesome. To show how delicate the balance is, in the summer I used to see algae increase rapidly; then I worked out it was due to the increase in duration and brightness of the daylight entering the fish room, so I now keep the windows well covered, and over the last three summers, problem gone.
It takes longer and it uses more effort for aquatic plants to assimilate CO2 from the water than from the air. This is why floating plants grow so fast; they have what Walstad calls the aerial advantage, of being able to take up considerably more CO2 and faster than the submersed leaf plants. And the brighter the light, and the more available the 16 nutrients, the faster the CO2 is taken up. Plants will photosynthesize full out, until something is no longer available in sufficient quantity.
My canisters all return the water below the surface. There is some movement in the area of the spray bar, but not further out. I have had heavily-stocked tanks, fairly well planted, run like this for 20+ years and never noticed any evidence of oxygen shortages. The rate of fish respiration is a good guide.
Byron.