Yes, I agree IRC logs have problems, in fact this is another reason why I, personally, don't like them. Nevertheless, transparency is everything and in my experience having logs available minimises conspiracy theories (which are inevitable in any succeful community).
The channel is open to anyone and the final decisions are published on meta, I think that's reasonably transparent.
Would it be possible for someone to set up a log bot (or whatever) on the IRC channel.
It's certainly technically possible. I don't know how to do it myself, however. There are some cons to public logs (it's nice to be able to talk freely without fear that your words will be used against you in the court of public opinion), but I think all in all it would be worth logging the conversations.