Not in the US, but in Europe it's more common. Shopping malls in Eastern Europe they're not uncommon.

only those that carry the shopping trolleys up/downstairs, designed so the wheels get locked into place.

I have never seen a flat one in anything else but airports or connections between other mass transit transports such as metros and trains. Definitely not in big box stores as they would be inconvenient and slower than pushing the trolley in the flat.