Because of practicality.
Because Halo 2 brutes were possibly of a different phenotype, sub species of Jiralhanae. They seemed more savage, didnt give a flying fang if they went all fur with some armored bits and pieces alongside a bandolier.
Halo 3 Brutes, I guess were another phenotype, more likely a jiralhanae subspecies. Think humans and neandethal differences here.
Halo Reach brutes might be the same as Halo Wars 2 and Infinites, still they hadd awesome tattos on their faces, especially on even lower ranking brutes.
HW 2 and Infinite, try to get across that only high ranking brutes, like chieftains are "allowed" to have facial hair and tattos as part of a ranking system.
Kinda makes sense.
The same thing can be explained regarding the differences between the other races species etc. Grunts, elites, jackals. I see all the different looks as canon/ lore but have reasons behind them why only those types of species appear here and there in game. Would be awesome to see for example HW2/ Infinite brutes command the more savage H2A/ 3 brutes or say the more aquatic, less armored sangheili elites come to terms with the classic looking elites from H2A, 3, HW2. The much more agile and seemingly intelligent, but eye color lacking elites from Reach could either be simply explained due to overall change in art style OR a rarer breed of Sangheili.