That's okay!
The first is an uncommon bug as others have mentioned. It happens maybe once a week for me. Kicks disappear nearly instantly before you can vote. I think this has been around since official server days. It was mentioned you can still vote with /yes or /no. A confirmation that you voted and how might be nice...?
Second - If this is intended behavior, it doesn't seem to work consistently. Sometimes players can go to the game room to change equips during kicks and come back in. I would think this should be allowed, as a game ending while a kick is on-going could risk a player getting kicked if they leave as the finish sign comes up. Not sure if they would get kicked automatically here. Also, the reason the fix was implemented, was because a player would leave the room entirely and avoid the kick, so it was impossible to kick them. If they're in the game room, it's still possible to kick them. So the use-case doesn't make sense to me here...
Third - Pop-up box for larger games makes sense. Still would hope for something consistent on this front.
Also as the others are saying, I'd love for us to be able to make "fake" kicks again with /vote kick <message> or /kick <message>