Is it really that they just log out? Here I was assuming they found some exploit or were deleting/recreating the character over and over. If they're just logging out, the blacklist definitely needs changed to let us add offline players to it. That's just terrible design.
I figure they're operating on "if they can't bl it, they'll see more messages." Obviously doesn't work for most that don't care anyway, but it's all about getting enough attention from those few someones that are willing.

It is indeed far more irritating to not be able to stop it so quickly/easily (which is again probably the goal for them). I've just had to adapt to leaving the bl prompt window open for 5-10 minutes before confirming. If they spam again, the window is already up and the bl usually goes through if you hit it near immediately. Or if you just wait a while to try, sometimes the character is back and can be added to the blist.