As long as a live game brings in better ratings than BTN live reruns we are going to see them soon on BTN.
I think you are wrong. Excluding opening Thursday night, here are the Thursday night games televised on the SEC Network:
And here are the games televised on the Pac-12 network:
True, the SEC network televised Western Kentucky at Vanderbilt on opening Thursday and the Pac-12 network televised UTSA at Arizona the same night. But that day has the most games of any other Thursday night because it kicks off the season.
Thursday night games are the domain of ESPN, CBS Sports Network, and Fox Sports because they have paid to televise most, if not all, of the games for the conferences. It is either show them on Thursday night or eat the game because of all the games they have the rights to cannot be televised on Saturday. The conference networks will not have that problem unless they lose the general sports networks (such as ESPN).