While this is a wonderful idea in theory, a key reason it's often not used for experiments is that there are just too many variables to control for (including, for example, the ongoing effects of spending a month wondering if you're taking something that's affecting you... which affects you in and of itself).
I agree it's not perfect, you're right to cite the Hawthorne effect. The vitamin D one for example would be affected by weather and seasonality. But I still think it would be really cool and a good product.
