Here's another way that 10-12 player teams can be indirectly encouraged:
The number of minutes played during a game should have an larger impact on their in-game GS.
Besides the minutes the player has been active in a game, the player's stamina and experience, as well as the team Attitude (Take it Easy, Normal, Crunch Time) should also have an impact.
For example, if a player stars with GS 9, if they have stamina of 5 they will lose 1 GS after 18 mins, 2 GS after 24 mins, etc.
If they have stamina of 9, they will lose 1 GS after 24 mins, 2 GS after 30 , etc... you get the point.
Similarly, the higher experience the slower the impact on GS, because presumably XP helps players better manage their in-game energy and intensity.
Attitude should also impact in-game GS: TIE might make a player start with lower GS, but it lasts longer because they're taking it easy. While on the other end, CT gives a player a higher starting GS, but deteriorates faster (higher intensity).
In other words, GS has a default curve based on in-game minutes played, and stamina, experience, attitude are modifiers.
And then, after the game, GS is restored by a certain fixed amount (or could also depend on stamina, experience, attitude, age etc.).
I would also argue that stamina should decrease by age, possibly drastically after a certain age.
Finally, it would be cool if stamina increased if players play more minutes and it should similarly decrease if players don't play many minutes. This can probably be implemented regardless.
If done correctly, it could result in a need for teams to have more depth, because a $100K sub with GS 9 would perform better than a $200K starter whose in-game GS has deteriorated to 5 after 40 minutes.
I'm sure there are several holes in this suggestion, and some of these ideas may already be part of the game, but putting it out there as a thought-starter.