At high volume the AM carrier needs to make larger excursions.
However at low volume (or idle) there's the question, What is carrier intensity? 50 percent? 100 percent? Your experiment suggests it's more like 100 percent, even though it might seem wasteful to use full power broadcasting silence. I suppose some carrier needs to go out on the airwaves, perhaps as an occasional beacon for aircraft. Or, to provide an indicator on radios which have a readout for strength of AM reception.