One data point for one specific Walmart:
I did a 3 night trip out of MSY over Memorial Day weekend. We drove to the airport on Friday to find all the lots and garages were full. We drove off-airport to discover all the private airport parking lots were also full. I didn't have time to drive home and taxi back and make my flight, so in a bit of a panic, I drove to the nearby Walmart on Veterans Blvd in Kenner, parked there, and called an Uber.
I figured I'd rather pay the tow fee, if that happened, than miss my flight and the wedding we were traveling to the next day.
When we got back on Monday, the car was still there, everything was fine. I think the roundtrip Ubers totaled to under $25, compared to $33-$57 that airport parking would have cost, so we ended up saving a little. But I didn't do it to save money, and I'm not sure I'd recommend it, especially for longer trips.