DHCP, RIAA, MPAA, and YOU!
DHCP works on a lease time - the only way you "lose" your IP address is if you are disconnected for longer than 1/2 the lease time and someone else gets it, or the ISP runs out of available IP addresses while you are off/dropped for a minute or two and you catch as catch can. If you are connected (router/modem, not necessarily your computer - sorry), you keep the same IP. In ALL cases, the ISP *knows* who you are EXACTLY. How else could they claim to know when you exceed bandwidth limits, eh? And just because you "never bring attention" to yourself does *not* mean that they aren't tracking you as a matter of course.
Marketers: Your IP address does not identify one individual, but a collective of consumers of one or more tastes at a residence. We collect the browsing habits of the user(s) at the residence to better serve you, and reduce the flow of inapplicable ads you see.
RIAA/MPAA: Your IP address does identify one individual, and any file sharing activity of copyright works means that you are a criminal and owe us money.
YOU: Alright @ssholes, one way or the other. Either it does identify me, in which case make the collection illegal and put protections place (makes it harder for RIAA/MPAA to track you because of privacy protections, marketers increase cost / lose business), or It does not identify me (RIAA / MPAA have harder time pushing a legal case, marketer's perceived value decreases).
Really, I don't see the problem here either way, eh?