Assuming it takes you 30 minutes for at least one of your weekly grocery trips, why would you make a habit of sitting in the car waiting for it to charge?
(1) I've been driving EVs for 8 years now and have yet to see a DC fast charging station at a grocery store. Electrify America uses Wal-Mart and Target as site hosts often, but not everyone does their grocery shopping there. Grocery stores mainly have L2 AC charging stations, which only put about 10 miles of charge in a car in 30 minutes.
(2) DC fast charging stations on almost every charging network will charge idle fees if you remain plugged in after you're done charging, or after a set time like 20-30 minutes, as they want you to move and let the next customer charge their car. So you need to sit in the car and move it when you're done, or it will become unaffordable.
Definitely some regional variability there, as this doesn't exactly match my experience, but it's close enough that I concede they are good points. To really get people on board who don't have good at-home charging available, there will need to be progress on both of those points.