To provide some figures for your point, Webvan was founded in 1999 when there were ~100M internet users in the US. Instacart was founded in 2012, when there were over 250M internet users. The success of these services is definitely a question of achieving sufficient scale to break even, which is much easier with a nearly 3x larger market.
Edit: Clearly it's not the only reason they've succeeded, they've smartly avoided all the capital infrastructure that Webvan relied on and mobile devices have improved tremendously but when you're talking about tenths of a percentage points in penetration, tripling your TAM is huge.
The major difference is not the size of the market. The major difference is that Instacart piggybacks on the existing grocery store network, meaning that they don't have to pay for the overhead of a big warehouse. That lets them scale up with their user base instead of having to invest a lot of money up front in warehouses.
So does Safeway. The trouble with doing this out of grocery stores is that the order system doesn't know what's in inventory, and some fraction of your items won't show up.
Amazon Fresh is doing this with their own warehouses and robots. They know their own inventory, and will probably crush these manual-picking operations.
Amazon has never had to deal with their own delivery fleets before, or perishable goods in their warehouses. While it's true Amazon has other revenue streams, Fresh is still just an experiment at this point.
It's a race to see who can take the market, and Amazon is taking a slower, infrastructure based approach. It will be interesting to see if they will see it through to the end.
http://i.imgur.com/44lkXHa.png
Edit: Clearly it's not the only reason they've succeeded, they've smartly avoided all the capital infrastructure that Webvan relied on and mobile devices have improved tremendously but when you're talking about tenths of a percentage points in penetration, tripling your TAM is huge.