If they provided larger meal sizes it would probably come closer. They'd be able to provide you one meal's type of food (less variety, fewer things to measure, and fewer types of ingredients = easier supply chain management) and you could get 5 or so meals out of one cooking session's worth of prep.
It probably still wouldn't come down to $7. But I assume there are people more willing to pay than me out there who would be happy with it.
I know I'd do it if I could lower the per-meal cost by buying more of the same thing. I typically do all my prep work for a whole week of meals on Sunday night so that cooking each night takes 10-20 min. I'd pay for a Blue Apron type service that saved me that work and the trip to the store. Plus, it would be somewhat more environmentally sustainable to ship a week's worth of food instead of just 2 meals.
But Blue Apron, as it is now, isn't cheaper or easier than what I do now and it's a nightmare of wasted packaging.