Your voice can only go as your vocal cords can take it. It’s natural for people who naturally talk low vs those that talk like phone conversation Nigerians.
It happens on most albums where quieter rappers go to any range that’s kind of extreme for them, or sing when they aren’t really singers. Common talks in a lower, quieter voice but he was rapping loudly in higher pitch.
He does it less on “one day it will all make sense”. It mostly stops after “Like water for Chocolate” because he mostly started rapping in a more relaxed, subdued way. The style had changed with the times and rappers didn’t have to pretend to be hyped up livewires all the time like 1991-1994.
Go back and listen to the difference in Nas, from “Illmatic” to “It was Written”. Ghostface doesn’t do it as much because he talks loud, but Raekwon’s voice broke sometimes when he was more animated. His style was mostly subdued though so it’s harder to tell.
If Schoolboy didn’t intermittently make his voice gritty his would do the same. Jay rock started doing it when he started rapping in his natural voice and being more animated (“90059” through “Redemtion”) instead of doing the forced deep, gruff voice. The examples are endless if you’re looking for it. Jay-Z still does it when he raps animated or goes outside of his natural speaking tone. It doesn’t have anything to do with drinking.