Choosing to destroy?
I find it interesting that you suggest that not logging the IP address is choosing to destroy it. Parts of my website run script to log who is visiting, but it does that by matching the IP address to a rough location (well, a country) along with, if available, the referrer. The IP address itself is not "destroyed", it is simply not logged. I don't give a damn who visits, I'm just interested in the general demographic of "oooh, I'm popular in <xyzzy> this week!". Yeah, lame, I know...
Perhaps The Pirate Bay's omitting of IP addresses was for similar reasons? The IP address is vitally important to the functioning of the Internet, but actually logging said IP address is not ... my site server offers *hundreds* of megabytes of gzipped apache log, I could trace every single visit and who did what right back to... God, 2005? something like that? But to be honest I'd just as happily switch that off and erase the old data. It serves no useful value to me, information overload. There's a gold mine of data of how people move around the site, what's the most/least popular, blah blah, but I'm not Amazon. The effort of ascertaining such information isn't worth the end result. Hence, I don't really actually *need* a log. I certainly don't *need* to be recording IP addresses (which I consider mostly meaningless anyway, as mine changes every 3-4 days). [you might ask why I wrote script to duplicate the apache log - easy, what I want runs to around 50K/month; apache's log runs to around 120Mb/month...need I say more?]
So, in short, there is a third option: simply not bothering.