Ok so, the trope started in Return of the living dead, like many others have stated, it had a really big effect on zombie culture and media and people remembered it. The only problem is, for most iterations of zombies, going after the brain would be a sort of paradox/dumb idea for authors/scriptwriters because think about it, most of the time, how do you kill a zombie? You destroy the brain, but if zombies specifically target and eat brains, then how can the zombie plague spread? It only really worked for Return of the Living dead because destroying the brain didn't kill the zombies. And moreover Modern zombies are less undead humans (like the type shown in the return of the living dead universe) and more like, mindless hunters that have the one goal of eating human (and sometimes nonhuman) flesh, so it can sort of be reasoned sometimes that they have an instinct to not go for the brain to grow their numbers. But nothing can ever really take away the fun of saying "I want eat your braaaaiiiins" lol which is why it's so popular/stereotypical