So, you can listen to Bleed, and the screaming bothers you? That song would be absolutely terrible without screaming, and I'll tell you why this is.
There is no melody to be found in Bleed. There is only a rhythm. Singing would be pointless because it doesn't add anything to the song, there is nothing to give the singing vocals any harmonic context and it would just sound like it was there aimlessly for no reason. And if you sit down and tap out the rhythm of his vocals, you'll find out it actually makes a lot of sense. In a way, it's like rapping. Whether or not you like the way he screams or not is irrelevant to the point that the vocal style suits the song.
Anyway, on topic, screamed, shouted, rapped, or otherwise percussive vocals are really something to be evaluated on a case-by-case basis. Either you like the way someone uses their vocal talent, or you don't. Screamers can sound amazing, competent, or less than stellar, just like any other form of vocalist.
And for those of you who say that screaming takes no skill, it takes HEAPS of skill. It's not as exact a science as improving your singing voice, but getting the right tone and most importantly learning to be able to do it for more than 5 minutes without killing your voice is very hard.
EDIT: Also, since the term "screamo" comes up often in these threads, let me reiterate that it does not refer to metal and even though it's a meaningless term, it usually refers to post-hardcore bands that use screaming. Most people use the term to refer to anything with screaming, and it has such a wide usage of different meanings that it has become irrelevant.