You can be sure that delivery fees will more than cover whatever the cost of gas, the cost of the driver, and the time it takes employees to shop for you so you aren't likely saving money, but the extra you pay may still be worth the convenience.

Have you been careful about making sure that the prices you're charged when shopping online are the same as what's on the price tag on the shelves? Online shopping makes it extremely easy for companies to overcharge you based on what they think you're willing/able to pay and provides them with valuable data they can use to decide when/how much to raise their prices.

You can also run into problems where employees will select for lower quality produce, and about to expire foods that in-store shoppers will commonly pass over. It's nice that it means less food gets thrown away, but can also mean you can end up wasting your money buying food you can't or don't want to eat.