While limiting the number of fouls that a player can commit during regulation helps ensure fair play, I think that it has unintended consequences if a game requires an extra period. Because starters tend to play the most minutes, they're also the most likely to get into foul trouble. So, while they shouldn't be rewarded for this, it seems unfair to have close games determined by which players are still eligible to play, especially when many calls are subjective.
To make overtime a better reflection of which team played best, I'd suggest giving each player an additional personal foul at the end of regulation. This means that if players had fouled out earlier, they'd be eligible to re-enter the game with one additional foul before fouling out again. Hopefully this would further limit the ability of referees to determine outcomes.