Maybe the problem with Walmart is they have a toxic brand for a certain market segment. Even with free same-day in-store pickup, I would still use Amazon's two-day shipping in order to avoid going into my local Walmart.
I currently live in a small mid-Atlantic town, and shop at Walmart for groceries because the nearest Target is 30 minutes away. Sure, there's some annoying customers sometimes with monster trucks or T-shirts with guns on them, but I don't feel like I'm going to be mugged. When I lived in northern New Jersey, that's exactly how I felt, so I didn't go to Walmart if I could help it. (But the nearby Target was great, so that's where I shopped for that kind of stuff.)
https://www.walmart.com/cp/free-shipping/1088989
There's also ShopRunner that comes free if you have an American Express card. You can use ShopRunner at a bunch of places like NewEgg, Drugstore.com, PetsMart, and more. Free two day shipping.