The reason for three mics when filming might have been this: Two for the PA, and one for recording.
It's still very common to use largely-separate signal chains for the PA, and for recording (and/or broadcast). These days we often do it with analog or digital splits, but analog splits can [still] be problematic and digital splits didn't exist yet back then.
Analog splits might have been particularly problematic when the source is two microphones fighting eachother. And it's often [still] the case that a microphone that works well for PA is not a microphone that is ideal for non-PA use.
(Sure, we like to think of live recordings or broadcasts as being "being there," but that's almost never actually the case. When recording and/or broadcast is involved, those things are often handled as separately as is practical -- often with gear and engineers that are outside of the walls of the venue.
This allows the FOH folks to get it sounding good in the room, the recording folks to get it sounding good on tape/DAW, and the broadcast folks to get it sounding good on radio/TV. They're different goals, and they've each got different approaches.)