It annoys YOU. Your preference absolutely would hurt immersion, just as it would hurt plenty of films.The vast majority of the Brazil sections of the game are utterly destroyed by not having subtitles. World building? Gone. Tactical advantages in combat? Gone. Details subtle and otherwise? Gone. A large amount of details of the plot? Gone.
It doesn't benefit the player, it doesn't make the game more immersive, it in fact ruins immersion, and it just annoys the player. There's no reason for it whatsoever and it provides absolutely nothing.
There's little strategy or variety in Max Payne 3, so I don't know what you're talking about. You're not missing anything gameplay-wise by not understanding the enemies, at least nothing that you can't already see. The enemies aren't very lifelike, and you kill them usually with the same playstyle.