I have been flying FSO for a fair amount of time and I am curious as to why aircraft assignments aren't rotated from frame to frame.
They are.
FSO squads indicate their ride preference for each of the three frames. Each frame CO does their best to accomodate each squad's preference for each frame.
Occasionally there is a sacrifice that must be made, such as assigning a squad to Torpedo bombers when they requested fighters, however such decisions are made in the context of the overall event (the squad that makes a sacrifice for Torpedo bombers one frame will not be asked to sacrifice again the rest of the event).
To completely answer your question, simply some squads do not want to rotate every frame. Some want to stick with a 190, or P40, or P38, or whatever. They are, more often than not, accomodated for.
Just out of curiosity, why do you inquire about this?