Maybe I'm missing the issue here. Is it about rotation, plane/mission assignment, who's in charge of particular mission within a frame, or something else? My impression is that you are advocating for a system in which everybody has to change sides so that it is "fair".
If I understand what you want correctly, then in my example from earlier in this thread, the first frame would look as I described it with 120 people who requested allied flying allied, 70 people who requested axis flying axis, and 10 people who wanted to fly allied having to switch to axis to make the numbers work. Remember that in this particular scenario, the numbers called for more allied than axis. Since this is Friday Squad Operations, let's go back to squads and say 3 large squads, 4 medium squads, and 4 small squads fly allied, while 2 large squads, 2 medium squads, and 4 small squads fly axis. 2 of the small squads that are flying axis requested allied but were switched to make the numbers work. So, right now, we have 10 people, or 5%, flying for the side they didn't want to fly for.
The second frame is where your system would kick in. Two of the large squads, 2 of the medium squads, and all 4 small squads who wanted to be and were assigned to be allied have to switch to axis. Meanwhile, all of the squads who were axis in the first frame switch to allied, including the 2 squads who wanted to be allied in the first frame but were forced to switch. Now we have 150 people, or 75% of the playing population, flying for a side they don't want to.
In the third frame, it really gets complicated. Now, both large allied squads who were switched to axis get to switch back to allied but, because there is still a large allied squad who hasn't switched, that allied squad and one of the large axis squads gets switched back to axis, meaning there are two large squads "unhappy". There are still 2 medium allied squads who haven't switched, so they both go to axis, meaning there are 4 medium squads "unhappy", and all 4 of the small squads who were switched go back to axis, meaning the original 2 small squads who wanted to be allied to begin with. That puts 90 people, or 45% of the population, in the "unhappy" group.
With this system, we can see that about 1/2 of the axis squads have to stay allied for two frames so that all of the allied squads have their chance to rotate to axis once. Remembering this scenario called for more allies, than axis, these numbers could be reversed - the smaller side is the one that will have to spend more time as the other. Regardless, we haven't achieved "fair" because some squads have to be "unhappy" for 2 frames, while some are only unhappy for one. From a numbers perspective, we've managed to make 100% of the FSO population unhappy at least once during these frames, and about 50% were unhappy during 2 out of 3 frames. That doesn't bode well for the future of FSO!
The reality is that normally, when numbers are off, they are off in favor of the allies. This usually means a squad that wanted to be allied is asked to fly axis. I can't speak to what the numbers usually are, but forcing a large allied squad to swap with a large axis squad does nothing to fix the numbers discrepancy. Forcing anyone who voluntarily flies for the less populated side to fly for the most popular side makes no sense whatsoever. In the end, it will come down to asking a squad from the popular side to go to the other side. If you don't want to be in that position, make a habit of requesting the less popular side and establish yourself as a team player there.
Regards,
Hammer