Whoops, I forgot my proxy.

As far as I know most users who use public proxies end up using ones that are found after 5-20 minutes of searching in the interwebs. Most of the time using these only compromises your security and privacy rather than the other way around.

..So why do people even bother using them? (Besides after getting banned in some site, I mean.)

Most public proxies are just random boxes that mindlessly gather user logs. Whether those can be used against you or not I don't know, but I don't think anyone gives a shit about a guy using a proxy to post in 4chan about animu, mango and general faggotry. CP is a whole nother story.