This is the sort of binary differentiation that has led to countless services being discounted on virtually identical criteria. AWS, for instance.
But it isn't so simple. I live in Canada and have used a couples of services and currently and semi-regular with makegoodfood (which I assume is very similar to Blue Apron). I'm a pretty decent cook and baker, have all of the cookware, and go to the grocery store relatively regularly, but still I make use of it because it isn't simply that they give me ingredients.
I like their menu. They constantly surprise me with good meals with great ingredients. Things that I would have never, in a million years, have chosen on my own. And the recipes (and thus, the meted out ingredients) have been almost perfect. This is a far cry from finding recipes online and replicating them -- this food vendor has been completely incentivized to make their creations perfect, versus recipe sites like AllRecipe where it's just user contributions, often with shockingly bad errors in some top recipes (pancakes with 3 1/2 tablespoons of baking powder to 1 1/2 cups of flour? Give me a break... 4.5 stars)
Cost wise there is no way I could go to the grocery store and buy the ingredients for less. I should say that I get the 4 meal versions (so the shipping is less a component of the price), but to get all of the often odd spices, small amounts of various things like odd ciders, vinegar, etc, it would be very pricey to replicate. Cooking interesting meals is expensive because you can't buy exactly what you need for most things. Not to mention that it wouldn't just be time consuming trying to find every oddball ingredient, it's stressful too. But every couple of weeks I get a box with very, very high quality meats, fish, perfectly portioned out spices and ingredients. It's so much nicer.
This is a bit like the "cloud server" versus "your own raw metal" discussions. In the end many underestimate the advantages of the former, and grossly underestimate the cost and inconvenience of the latter.