In my mind the point of calling it a "rootless voicing" is that even if the bass player does play the root, not everyone has to. Playing a rootless voicing is a choice to be made on the fly given the knowledge of the root, melody and key, rather than something you'd typically want to prescribe. It's a matter of interpretation. The listener will often have the root in their ear (the mode really) even if nobody is currently playing it explicitly. Or maybe someone just played the root and nobody is now but the rootless voicing still rings. Or maybe the last chord had the same root and the sense of it is lingering. Or maybe the root is in the melody.

If I couldn't have any information about the key, I'd still want the root and the melody.