The entire purpose of the modern economy is to pay other people to do things so you don't have to do them yourself. Did you build your house from trees that you chopped down yourself? Do you grow all your own food? Do you cut your own hair?
If you think it's worthwhile to do your own grocery shopping, then you may do so. But there's nothing wrong with paying someone else for a service.
You presumably pay people for their skillsets. Screwing a light bulb in or doing your grocery shopping doesn't require a special skillset. There are some tasks that just aren't in the same ballpark as building homes, growing food, and cutting hair, and I think shopping is one of them.
If you think it's worthwhile to do your own grocery shopping, then you may do so. But there's nothing wrong with paying someone else for a service.