Anime faces seem very easy to draw. Granted I don’t watch anime, so I could be missing something, but it’s not like they are going for photorealism.
Are big noses flattering? No. Are they hard to draw? Yes. Get rid of them!
The abstraction also means that you can change things up for emphasis (really exaggerating features, pushing extreme expressions, or switching art styles entirely) without it being as jarring as it would be if the characters were photorealistic