Happy Jack made the very good point about the people who just mumble into the mic between songs - those cases may as well just be "dead air" between songs, for all the good they do! Whoever gets the job needs to lean into the role, become a bit of a circus ringmaster, if you like. Loud, clear voice, as if you're doing theatre (dahling!), and if you keep it short and punchy, you keep the audience engaged. Have some good lines planned ahead of time if it helps. If you can nail it, I can't imagine the band would sustain their objections.
If you need inspiration, Pete Townshend did it very well around The Who's creative peak. Look up one of their (better) live recordings (Isle of Wight 1970 is a good starting place) and skip to the breaks between the songs. It's often daft, even a bit camp, but it helps to maintain the energy.