Communication is more than written English, it may not even happen in English at all.
Furthermore, it's fine for lots of employers to care about your English-grade. If they care about that, let them look at that.
Why force everyone, even the people who do -not- care about English-skill, to consider it anyway, because you put some fraction of it into every other grade ?
I'm not saying English-skill should not count. For a lot of jobs, especially in English-speaking countries, it obviously should count for a lot. I'm saying that your level of English-skill, should be reflected in your *English* grade.