I think it would help. There are other places in the act where they also refer to “personal uses”, “private use”, and “private purposes”, and I think there's another one too, which I can't remember just at the moment. But all these things seem quite vague, and we should stick to the same language to be consistent in the bill, if it has the same meaning.
But quite apart from that, in that context of making this copying for private use by individuals or anybody, that still isn't clear what it means. Can I send it to my friend? What can I do with it? Maybe I can't. I guess we have some interpretation of the “private use” regime now, but it's a different kind of copying, so it isn't really clear what it refers to.