It was really: enter your bank account credentials and get instant visualization of what you spend your money on. Useful, but hardly life altering for most people. "Wow, I spend a lot on eating out. I should cook at home more."
If you really want to be the Mint.com of food you would create an iPhone app that OCRs your restaurant and grocery receipts and displays cool charts of what types of food you eat. "Wow, I eat a lot of unhealthy food, I should cook at home more."
I suspect the solution to the problem you've identified doesn't look anything like Mint.com. The startups that are delivering pre-made meals are probably closer to the mark.
It should be possible to affordably deliver quality food to people's houses on a bi-weekly basis. You could take into account all requirements you specified.
You get a package, open it up, drop the meals into a pot/microwave and instantly get a fresh healthy meal. That's the only real "drag and drop" solution.