I feel like grocery stores could easily compete with blue apron for much lower costs. Just ration the food they already have in stock in little packages. Charge a little more than you would otherwise for the employees time picking recipes and combining them into the packages. I would happily use this service at local grocery stores. But compared to grocery stores and cooking from scratch blue apron is too expensive for me.
edit: Blue apron is currently $7.50 - $9.99 per serving. I cook delicious food for myself regularly for less than $4 per serving if I make enough to have leftovers for a day or two. It really seems to me that grocery stores could eat blue apron alive with their lowered costs to provide this same service.