Playing devil's advocate, the all-in cost of a short commute is likely higher than that for grocery delivery.
Let's compare a White Plains, NY <--> Midtown Manhattan commute to an Instacart delivery. That commute takes about 1 hour [1]. The average 1-bedroom in White Plains goes for about $2,270 a month [2]. In my neighborhood, Flatiron, it goes for $5,660 [3]. Let's assume 260 working days in a year [4], i.e. 520 [5] hours of commute. That $3,390 difference in monthly rent comes out to $40,700 a year, or $78.30 per hour of commute.
By coïncidence, that's what this guy on Reddit [6] estimated Instacart's markup to be. You'd have to order $87 in groceries (i.e. $150 on Instacart) twice a day every working day to come out even against a 2-hour-a-day commute between White Plains and Midtown.
[1] https://www.google.com/maps/dir/White+Plains,+New+York/Grand...
[2] http://www.apartmentguide.com/apartments/New-York/White-Plai...
[3] http://www.apartmentguide.com/zip/10010-Apartments-For-Rent/...
[4] http://www.answers.com/Q/How_many_work_days_are_in_a_year
[5] 260 * 2
[6] https://np.reddit.com/r/boston/comments/5xj47l/ever_what_ins...
No, I'd rather spend that time playing with them @home or park.
I walk to the supermarket every day (which is about 10 minutes each way), and probably spend 10 minutes wandering around inside even if I don't need to buy anything (I'll find something to buy), just to stretch my legs.
For sure if I spent over 30 minutes each way to work, I'd be less inclined to spend a lot of time at the supermarket.
As an aside, if you ever find yourself in a situation where it's possible to do this, I highly recommend taking the plunge, even if it means paying a bit extra in rent. It's been life changing for me.
My daily "commute" is a few hundred feet, and it's really changed my life. "Ugh, I've got to go to _x place_" suddenly sounds ridiculous when that place is a 3 minute walk away. You can wake up later, have more time for everything else in life... it's very nice. Sure, you might have to take a smaller place, but I'd rather have a small place that I can spend time in than a large place I never see.