besides not making any difference? ... it will still be possible for your ISP to identify you ... most basic reason: accounting. No access without clear identity, otherwise internet access would be free!
anyway, I think that this topic is rather misplaced in this hardware support forum...
if you are on a cable modem, they have lower level identifiers (including their own mac) that can easily tie you back to your router mac and therefore IP. those you can't change unless you buy a new cable modem, in which case you have to call up the cable company anyway to get that mac authorized.
but yeah, this doesn't belong in the announcements forum