Right after I read this, my immediate reaction was to feel kind of annoyed at the author. A little superficially, no tech or design talent in house, no food industry experience, and not much marketing and sales expertise, so what exactly does he bring to the table here, besides really wanting a startup?
Also, this idea hits on one of those things that lots of people really want to believe that they would do - cook their own healthy, organic, gourmet, etc food - but very few will actually take much initiative to do on their own. That doesn't necessarily mean that it isn't viable, but it does mean that your big challenge is going to be marketing and conversions - getting people to go beyond saying things that basically mean "I really want to believe that I am the kind of person who would use something like this, even though I'm not", and actually buy the product regularly.
After thinking about it some more and reading some of the posts on here, this might be a viable idea, but it's going to need a lot better marketing to go anywhere. A few ideas, some stolen from other posts, mostly in an attempt to exercise my own marketing-think muscles:
Make the product stickier - try to sell a recurring plan of a meal a week that has to be explicitly cancelled. Or at least email people who have ordered regularly to suggest new meals for them. You do have new, promoted meals, right?
Have a spread of products, from things that just require heating, barely a step above microwavable, though mild prep, up to things that may require an hour or 2 in the kitchen to make. See which ones sell the best, and emphasize those.
Try to partner with anybody involved in cooking or recipes with an audience in the area. If they're on the web, make it super easy for them to submit ingredient lists for their recipes to you, then an easy way for them to put a link on their site for "Get the ingredients for my [whatever] delivered to your door today with Dinnr!", with affiliate payments for orders. Now you're helping them monetize their sites too, so they have a good incentive to work with you.
In person, too. There's probably some cooking classes in the area. Get those classes to plug your site for their students to get ingredients for an affiliate fee.
Get some cooking experts on staff, and start producing your own youtube videos and blog content on how to cook things, with an emphasis on explaining the basics for newbie cooks. It would probably help you make sure you're actually getting good quality ingredients too.
Make social connections. Make a way for people to tell their friends on FaceTwitInstaPint that they just cooked X, and it was awesome! It might even be good to make it so that they can only order basic things at first, and they get points or something from cooking them, which will eventually make them eligible to order the more advanced things. They can brag about how many Dinnr points they have. They can see that they're either getting more than the other guy, so they can think they're better than them, or they aren't getting as much as somebody else, so they need to order more stuff. Then you can suggest new meals, too, based on their skill level and their preferences.
The real pain point isn't shopping, getting ingredients, or throwing away unused ingredients. It's wanting to be seen to their social circle as the kind of person who cooks awesome stuff. Figure out how to hit that, and you'll probably sell.