My rinky-dink experiment (inconclusive at best imo but w/e):
The O2 monitor does not have a 'probe' but is a small handheld unit with a built-in sensor so I couldn't use a flask, I had to use a 4L beaker in order to get the monitor inside the 'fermenter'. I put about 1" of water in the bottom with a stirbar and placed it on a stirplate. I did not have CO2 (or dry ice) so I ran some plastic tubing from an inert gas source to the bottom of the beaker. I hung the portable O2 monitor such that it's sensor was facing the water and was about 1.5" above it. Then I covered the beaker reasonably tightly with foil (we'll change this later). The gas tubing and the tie-wrap I attached to the O2 monitor prevent a good seal at those two points anyway (I ran the gas tubing out of the pour 'spout' of the beaker).
At first I used GN2 because it was most readily available. It might be interesting to note that when using GN2 I had to use an unreasonable amount of flow just to purge the O2 out of the beaker and when I reduced the flow the O2 level went right back up. So I checked the molecular weight of GN2 and found that it is almost exactly the same as air (and ever so slightly less): GN2=28.01 and Air=28.97. The molecular weight of CO2 is significantly higher at 44.01. One other inert gas I had available; Argon, has a much closer molecular weight to CO2: Ar=39.95. So I switched to Argon and it was WAAAAY easier to purge the beaker and keep it purged.
First I purged the beaker by flowing faster than any reasonable starter fermentation. That got it down to about 0.3% O2 fairly quickly/easily and I didn't try to go any lower. Then I dialed back the flow to what seemed like a reasonable 'high krausen' bubble rate. Then I waited to see if there was an equilibrium point it would reach with no stirring, just some bubbling (within a reasonably short time frame). After about 30 minutes it was at 0.6% O2.
Then I turned on the stirplate and got a nice vortex, considerably more than just a dimple on the surface. After about 30 more minutes the monitor read 0.9% O2. Then I loosened the foil (stirplate still going) and the monitor climbed all the way up to 3.0% O2 in just 15 minutes.
The beaker obviously has a much larger opening at the top (7“ diameter). I had way more headspace than what most of us would have in; say a 2L flask; and the liquid level was much farther away from the top than a typ 2L flask starter. What the combined effect of these are I don’t know. The larger opening should allow air in more easily and the larger headspace should make it much harder to purge out the air. Also, a fermentation has CO2 coming out of solution over the entire surface, creating a more even upward ‘push’. The gas tubing in my experiment was bubbling against one side of the beaker so I would think that created some small ‘currents’ in there. I pre-purged the beaker with Argon which doesn’t happen in a starter fermentation but we usually have WAY less headspace (i.e. less gas to purge).
So I'm not sure if this showed anything other than:
The fact that CO2 is much heavier than air makes a huge difference in how much air remains in and gets into a flask of fermenting beer.
Covering your starter loosely vs. tightly does seem to make a difference.
Obviously, there is
some rate of fermentation that would drive off all the initial air and would prevent any air from getting in (eg - otherwise chemists couldn't work with hypergolic substances in plain ole lab exhaust hoods and have the toxic vapor detector never make a peep

) but I'm not sure if we reach that rate.