Well so far both P1 and P2 has faced their final combatants without stealth (not really by choice though). But I guess it does give them an advantage when they're facing bigger and heavily armed groups. Remember that they're still hunters, and not really warriors. They have some honor, but I can't blame them for using everything they got to capture the trophies they want.
At least P1 activated the self destruct after he was completely and utterly defeated and literally on the brink of death. P2 was just hanging on the edge of a building with a high chance of survival and an incomplete hunt. Yet he was just gonna Kamikaze himself along with his main opponent in the middle of a city. That's pretty douchbaggish IMO.