I actually do know someone who regularly hits up multiple grocery stores every week chasing deals and that does seem crazy to me. The cost in gas and time doesn't at all seem worth it.
The time saved is enormous, and the amount of money we might be saving by being more scrupulous is probably on the order of 5-10 bucks/week, which granted does add up over the course of a year. I like to think it’s a wash with the gas/car maintenance we would be spending, but who knows how accurate that is.
Works well enough for us, at this stage in life. Walmart is on the very cheap/low quality end of the spectrum, and we cook all our meals/pack lunches.
Always open to new ideas as it relates to saving money and being more efficient with time. These kiddos won’t be kiddos before we know it and we try to optimize our time with them as much as we can.