One easy test-case would be to look at WN. Do they have a higher number of checked bags/lower number of carry-ons than the legacies? I haven't flown WN in years so can't comment from experience there.
My pet peeve is when passengers complain "I get free bags on Southwest" and I bite my tongue before explaining that there's no such thing as a free lunch, the cost is internalized elsewhere, and that causes them to mishandle more bags.