My understanding of the NBL rules is that it is only in the last two minutes.
Your understanding is, as usual, wrong.
It can be used at any time in the game to check the value of a shot, what time should be remaining on the clocks if there's an issue, or to identify which player should be shooting free throws. It can also be used after fight/melee situations.
It can be used in the final two minutes to check whether a shot was released before the shot clock or game clock buzzer, whether it was released before a foul call, and to check possession on an out-of-bounds call.
ut in answer to the OP, yes I would give each coach 3 appeals, 1 in each half, and one in the last two minutes. With the condition that if the appeal is upheld, then they get a 2nd, but no more than a 2nd in each period, so an absolute maximum of 6.
Systems where you lose challenges whether you're correct or not are absurd.
I would also restrict the type of call that can be appealed. OOB, blocked shots and reaching in where the player claims he got all ball, 2/3 point calls, and buzzer/SC beaters.
So when you say 'restrict the type of call that can be appealed', you mean 'massively expand the types of reviewable calls, including making subjective calls reviewable unlike any other sport in existence despite the obvious impossibility of reviewing them'?