I don't like keeping a player on the floor with 2 early fouls because it messes up your defense. The player must play cautiously knowing they have 2 fouls, so they can't challenge shots, work over screens, or even box out as they would normally. It also effects the entire team defense because the player can't rotate as aggressively and the player can't help as they normally would. When you are defending a screen and roll and the other guy is basically useless because he can't close out on the shooter, hedge or really anything that might risk getting a cheap 3rd foul it screws up your whole defensive plan. It's not like you can hide the fact a guy has 2 fouls, there is that giant scoreboard glaring at you from center court with that big 2. Every good coach will make sure all his players know that, and whoever is matched up on that player should be attacking them at every opportunity.
Then there is the human element of the game. We have all played in games when your head is just not on quite right. Often these are the games when we get into foul trouble because we are making mistakes. Getting called for fouls is frustrating, especially when you think they were bad calls. Getting tossed back into the game after getting 2 fouls when you are already frustrated is a recipe for making another mistake.