I really can't contribute anything regarding the tape delays or when most of the games started being broadcast. I do remember watching tape delays, I think in the '70s.
What I also remember is when the games were on the radio. Prior to the plethora of games on tv, the SEC schedule was such that the teams would only play on Saturday and Monday nights. One week UK would be at home, the next week they'd travel. They would go to Mississippi and play Ole Miss and State. Then the next week they'd be at home for two games. They'd go to Louisiana and play LSU and Tulane, which was in the conference then. Next week they'd be home; Seems like I remember Georgia Tech being in the SEC because it seems like UK would play Georgia and then Tech. Maybe it was Georgia and then Florida. Can't remember who was grouped with Ky, maybe Vandy. By grouping the games it cut down on their travel. I don't think they traveled by plane back then. Also, without the TV time outs, games lasted 1 1/2 hours unless they went to overtime. Sometimes, if there weren't a lot of fouls, which was about the only thing that stopped the clock, a 20-minute half would be played in 1/2 hour.
Anyway, I don't have the inclination, but if some one wanted to search Jon Scott's excellent website you could probably see when they stopped playing this Sat/Monday schedule. They had to end it for TV, so that's when the games started appearing on TV more. I also remember that the home games could only be telecast on the delayed basis. Live games, which were occasionally broadcast, were always away games. Does anyone else remember it that way?