The oily film in aquariums is typically a biofilm, that is associations of bacteria, fungi, algae, polysaccharides, etc.
It may limit gas exchange, which as you mention can function both ways, help keep CO2 in, limit O2.
It will also reduce the light penetration as it is effectively a filter.
It increases the organics released in the water which might favor BBA.
Now, this last point is worth discussing more. The reason why you have surface biofilm is because you have enough food for bacteria in the water to start with. Of course if you have stagnant water you will get a little water surface biofilm but the (re) generation time is long and thus unlikely to be a problem in aquariums with fish and some pump. I noticed the biofilm becomes thick when there is an abundance of ammonium. Another more whitish biofilm is present when plenty of iron is present.
Thus, the biofilm tells you there is an abundance of bacteria nutrients in the aquarium. Removing the source will reduce the growth rate of the biofilm. As you mention increased surface turbulence, skimmers and fish that eat it (guppies, platies, mollies) are good ways to keep things in check.
Sent from my ONEPLUS A3003 using Tapatalk
On hiatus till later this year