Normally yes, but NYC is sort of the Big Exception in the US - it's the only city in the country where the density is so insanely high that I can imagine niche delivery businesses surviving.
We've seen this with eBay Now - the economics are sustained by limiting service to only zip codes with sufficient density.
I agree. The main problem with the original idea, IIRC, is that the product is cheap and heavy-- low margins and high shipping costs. The consumer was simply better off getting it at the store.