Are a mixed blessing. Seriously.
1) They give you time to sit back and realize what you've done.
2) They give you incentive to play with sub-optimal champion combinations because you've dodged three times already and d*mned if you're going to wait 25 minutes for that stupid timer to wear off.
3) It encourages you to troll your hardest to try and get somebody else to dodge. Always a good time! Who isn't afraid of a Revive/Ghost Kayle demanding "mid or feed", and generally insulting people. The key is not to be so idiotic that people will queue with you anyways, but to be so horribly obnoxious that they can't imagine spending another 10 seconds with you, let alone another 30+ minutes.
4) It makes the people you've dodged move on (with any luck) so you get a refreshed pool.
I bring it up because I randomed up Amumu after I was the last one to lock in. It gave me that bug where it automatically assumes that you want to "Finish What You Were Doing" instead of giving the option. By the time I got there, there was an Irelia and Pantheon locked in, and the Irelia demanded a tank. I decided to random.
"Bad luck," said I, "I randomed Amumu."
"It's not too late," some guy interjected, but I refused.
"I cannot deny the bond of random!"
And so I dodged, unable to subject an unwitting team to my awful, awful Amumu playing. Seriously, I'm that bad.