I agree with a lot of this:
1) I don't like stamina drain associated with arm trap at all
2) It should be more difficult to arm grab (and especially hold onto the arm) for a tired fight on bottom of mount
3) However, if a fighter who has stamina traps your arm then the bottom fight should be able to be dangerous from the bottom. Of the arm trap from mount they should have an increased chance for a reversal (into top of closed guard) or to escape into half guard)... And if you arm trap from bottom closed guard, the guard player - with stamina and GA - should be able to go for sweeps or attacks)
So yeah, I hate the stamina drain because it has no connection to reality. The above things I outlined are more realistic and hopefully explain the more likely scenarios of outcomes. Generally speaking:
1)Tired people who trap the arm are defensive and breaking posture. It should be fairly tough to keep the arm trapped (depending on grappling skill and stamina difference between the two fighters)
2) a fight in bottom mount who traps arm has ability to reverse or escape to a guard
3) tired fighter in bottom guard (see is breaking posture and saving energy until they can escape or attack)
4) bottom guard player who has stamina and traps arm becomes more dangerous and can attack
Get rid of stamina drain when it doesn't tie in to real life!