For TDs I can see a free game mode selection like this to be trouble. At least for multi-player games. Who should a player pick? And who. And why should this player be granted this priviledge.
If selection to be chosen is decided by TD, but still up to the players to do, what if some games are started or even playered out on the incorrect mode. What a mess.
Fixed selection it is. But of course the best solution is to have it in the menu. 8 ball, 9 ball or free.