A specialty shop can probably survive Costco much more easily than they can survive Walmart or any other conventional (American) grocery store. The grocery store carries 20 or 30 different olive oils, to select one example. Odds are all the snobbiest will find something they like... odds are even decent that in a blind taste test even the snobbiest would find something that they would be horrified to discover came from a normal grocery store.

Costco carries one or two options for a given thing, and are outright missing many things you might want. As nice as Costco is for buying things on a budget when you're going to use them up fully, I think it would be a bit of a challenge to make them your only grocery source. Doable as a sort of self-imposed challenge, no problem, there's certainly enough for that, but you'd be missing a lot of things, and/or wasting money on huge quantities of things you won't use. The quality is generally pretty decent (I may have more brand loyalty for "Kirkland" than almost any other brand) but not necessarily the most premium options. If you are the type to even consider the specialty shop in the first place you're more likely to be unsatisfied by Costco than a grocery store.