The "tape delay" thing is a little overblown.
In 1980, for instance, there were six games in the NBA Finals. Three were shown live everywhere, two were shown live in Eastern and Central time zones, and for Game 6 affiliates had the choice of showing it live or on delay.
NBA shares some blame for this by starting its schedule much earlier in 1979 and 1980. That resulted in Finals games being played during the May sweeps.
1978 Finals ended on June 7.
1980 Finals ended on May 16.
1981 Finals ended on May 14.