Amazon has had, what, five years to expand its Amazon Fresh grocery delivery service? The fact that they have chosen not to implies that they haven't managed to make it cost effective. I think this speaks volumes about the feasibility of grocery delivery.
Yes and no. One thing to keep in mind is that Amazon is a highly diversified company. So even if expanding Amazon Fresh to other cities would turn a profit it may not be worth it to them to put resources behind if it won't be able to turn as much profit as, say, expanding amazon proper to other countries (which they're doing) or building out the cloud business, etc.
My takeaway is that this is not profitable on the global or national scale, but on a local or regional scale, it can be. Amazon might not want to pursue a strategy with limited scalability, whereas Instacart might not even need to worry about that.