It changes the way the audience feels about Travis irreversibly. Even if you cheer for the guy, thinking "yeah, those fuckin scumbags had it coming," you have to acknowledge the fact that it was heading towards ending with him assassinating the candidate, which can't be justified.
It's so extreme that it just knocks you on your ass. It still does for me and I've seen it a bunch of times.
The look on Deniro's face when the cops come in, the banality of the letter from the girl's parents, the return to normalcy, the list goes on.