Why wouldn't you? For the average site (like the one mentioned in the OP), it really doesn't matter who handles authentication (not authorization). Now let's leave banks and websites like that out of the question. Digg? Slashdot? Perlmonks? JoeSchmoe-Forum? Does it really matter who handles authentication?
To me it does matter. If it's not secure, somebody could easily log in as
moritz, and with a few writeups could destroy the reputation (and perhaps even trust) that I built by writing more than 2000 posts. (By reputation I don't mean XP right now).
Loosing the account would be very bitter, and I'm quite sure that frequent users of other sites think similarly.
If a site isn't important to you, you can post as Anonymous Monk or "Anonymous Coward" or with a bugmenot account. If it is important to you, then security matters for you.