I think "be friends with" is so common as to count as an established idiom.

My guess is that it originated as children's usage. It is possible that young children heard such expressions as "let's be friends" and subconsciously interpreted "friends" as a (predicative) adjective, which could be used with a singular subject also.

The usage could then have gradually spread to older age groups. But to my ear it still sounds vaguely "juvenile", despite its common use by adults.