As it turns out, not everyone is listening using a modern device. When we tried VBR a significant number of people could not listen because their MP3 playing hardware/software of choice did not support VBR files properly. They didn't realize this was the problem. They just complained that the file was corrupted while it was working fine for everyone else.
Also, lots of encoders, including Adobe Audition/Adobe Media Encoder, don't write the headers on VBR files properly. This also causes a lot of players to fail at playing them properly.
https://forums.adobe.com/thread/1072786
When you make a podcast, maximum compatibility is the priority over audio quality and file size. So standard old MP3 it is.