Sorry but it is.
It would actually ruin immersion and is not realistic at all.
When you get hit, there is no reason why should there be blood in your eyes and even if somehow blood does get in your eyes, it would only blind you, not give you a bloody screen effect.
This also ruins immersion since bloody screen would actually make it look as if there was a camera instead of a person and would actually be a slap back to reality.
Not to mention that it would result in unnecessary gore.