They are SOMETIMES identifiable information. They are not RELIABLE for identification.
If you are going to be collecting information, you are not going to choose unreliable information when you have the option to collect reliable information. That would not make sense.
I can right now open my vpn, change my ip address, go to my apple account and it will report that my Mac is "Online", meaning that apple knows that my particular machine is on with a given IP address. It would be completely useless (redundant at the very least) to also include the uid in the signature file.
There might ten other, a hundred other people with the same public IP visible to Apple, if you ISP is running you through a NAT.
That fact that you have connected from an IP recently in no way guarantees that the next connection from that IP will be coming from you. That is exactly why you need to send an identifier for any data being collected.
If you are going to be collecting information, you are not going to choose unreliable information when you have the option to collect reliable information. That would not make sense.