It looks unnatural in an odd way. I guess that's what I really meant initially. There are exceptions of course but generally speaking having it match makes it seem like it belongs that way.
A lot of examples for things that seem more naturally pleasing and more inherent than the other side which doesn't match hair/eye color. I think these are probably the best when it comes to if the eye color was changed, the character design wouldn't be as good as it is for most people. I don't think any of the girls here would be more popular if they had red eyes(or any other color for that) instead. Using Blue Archive girls for no other reason that it's that it is the only gacha I play and am familiar with. Most of the girls from it with red eyes also have black or white hair too.