A ready check initiated after the last champion is picked with a timer of 10-15 seconds wouldn't make the game that much longer of a wait, hell I've waited 3 minutes at the loading screen while someone loaded into the game.
Here let me elaborate on my suggestion since my obviously pretentious answer to a commonly occurring problem seems to have caused you some distress.
Problem - People afking a game after picking their champion. This allows the game to start and there to be a 4v5 match-up, which are at times winnable, but still this will result in an unfair advantage to the team with 5 champions giving them more control of the map, pressure to apply to lanes, and all in all just an unbalanced matchup.
Solution - Ready check after the final champion is chosen to insure that everyone is still in the lobby right before the game begins to load.
Result - More balanced match-ups with a less likely chance of getting into game and realizing that your jungler/toplane/midlane/whoever are not present. Penalties applied to the person who is not present for the ready check, allowing your player base to not have to be penalized for dodging a game where they will be at a significant disadvantage, and a happier community.
Apparently 15 more seconds after champions are locked is too much to ask, obviously Mackle will die if he has to wait for 15 more seconds, so we should probably not add in this feature to make everyone else a bit happier and more sure of their team. Sorry about that Mackle.