When someone gets disconnected the user experience is very poor and unfortunately, disconnects are not unheard of (nature of the internet).
1) When someone stops responding it takes quite a while before the disocnnect dialog comes up. This means the game is just "froze" but you can still chat during this time (so I'm guessing chat is out of band which I will bring up later).
2) Once the disconnect UI does come up, there is an eject option for all players, not just the one who is timed out. It does indicate who is timed out with the "quiet" column but for a non-savvy user that doesn't mean anything and they'll most likely just click all the buttons or none of them, not knowing what they are doing.
3) When someone times out for 30+ seconds there is really no need for the other players to have to do anything to kick them. They aren't coming back. This isn't 1990 anymore where you could go silent for 30+ seconds and still be connected (just lagged).
4) Chat is disabled while the kick dialog is up. This means that when the dialog doesn't go away after you click the eject button on the lagger you have no way to communicate with the other players to try and establish what is going on. In the last game I was in someone D/Ced and when the dialog came up his teammate left so we were left with a dialog up and no one quiet (lagger was ejected, the guy who left was not technically "silent" yet). Since chat is out of band there isn't really any good reason to disable chat while that dialog is up. In fact, I would argue that chat during that dialog is one of the more ciritcal times chat is needed between the teams so players can figure out what is going on (especially the non-savvy users).
5) If you insist on leaving the eject dialog in then at least make it so there is some feedback as to what other players are doing. Perhaps a counter of how many players have opted to kick who, etc. As it is there is no feedback at all except the button disappears.
6) Once the dialog does go away the game resumes immediately. When you just waited 30 seconds for the dialog to appear and then another 15 seconds for the ejection process you aren't exactly "in the game" anymore. I was alt-tabbed out browsing the web at this point (again, due to the lack of feedback as to what is going on) and then the game just starts all of a sudden in the heat of battle. It would be nice if the eject dialog would go away and then the game would be paused for 3 seconds or something so people can get their bearings back.