I think it's a little more nuanced than "bands/producers don't care" and a bit more complex than "exporting the audio (that already exists!)".

Directly exporting the audio straight from the mixer would not necessarily produce quality recordings because the audio there is tuned for the purposes of sound reinforcement. To properly record a live concert requires an entirely separate setup with their own microphones and then some direct output from the mixer on a per channel basis to allow for post-production editing.

And a lot of people don't care about that! Lots of people are happy with the quality you'd get straight from a cell phone microphone.

But the people on stage and the people in the industry ... they're the ones actually involved in producing the sound, and many care very deeply about the quality that gets recorded and then shared. That's not to say that all musicians are like that, but many are!