Challenge will be that folks who shop at Whole Foods (aka Whole Paycheck) are already relatively price insensitive compared to people who shop elsewhere. Instacart was such a good match for WF because it's the same demographic of people who are willing to pay a lot for convenience. Your average Publix shopper is likely to be much more price sensitive.
Whole Foods is reasonably priced for actual food. They just have a different approach to high-margin products where instead of Twinkies they sell you special homeopathic Twinkies.
I call BS. I really like Whole Foods, but they are WAY more expensive to fill a "normal" grocery list than a place like Publix. Granted, a lot of that is because they only sell more expensive versions of things (e.g. sometimes organic-only produce, and their meat especially tends to be much more expensive), but it's still very difficult to shop cheaply at WF.
Instacart's service model, which allowed them to scale up really fast and cheap, should also allow them to scale down fast and cheap. They still have a brand, customer relationships, and demonstrated credibility partnering with retailers. I'd say the company will be fine, but many of their workers will face tough choices soon.