I think that for the most part, baggage carts, other than those used by Red Caps, have become a rarity. The cause? Wheeled luggage.
Another culprit? The money boxes for carts that required a dollar or so to be inserted to free a cart were vandalized, essentially wiping out the income of the owners. Damaged or lost/stolen 'free' carts owned by Amtrak likely contributed to their demise as well.
These days, almost all larger luggage that I've observed has wheels. And those that don't, quite often has a separate fold-up cart underneath. The days of schlepping big suitcases without wheels is largely gone. I don't recall seeing any for sale in the past 20 years or so that didn't have wheels.
As for NYP, CHI, and other locations with red caps available, I'm sure they like getting some business, and the tips that go with it. Hence, no carts.