Sounds like a good balancing act to leave 3 feet of stalk. Leaving everything on the stalk means slow decomposition, giving opportunity to pathogens. Fast decomposition by chopping it up allows proliferation of aerobic bacteria, crowding out pathogens, also traps nitrogen/water that might have evaporated. Simple A-B test remains potentially informative, comparing root mat size after several seasons for two cases: no cutting of fruited stalks versus cutting them up. If the root mat absorbs most nutrients/water from uncut stalk, we save labor as a bonus.
As an aside, our Gran Nain yard bananas taste better than industrial bananas. We think because we mulched with lots of tree leaves/branches, etc. People around here are experimenting with big mulch piles (for everything, not just bananas), not even bothering with compost anymore. I think this ensures nice ecosystem under there with abundance of all nutrients except possibly nitrogen. And like you, the companion plantings and ground covers never seem to compromise the fruit trees.