Their distribution network is heterogenous. Not all facilities ship orders to customers. Not all facilities that do ship orders to customers stock all product types and sizes.
Last I checked they were optimized for 2-day delivery. I imagine their 1-day delivery logistics are not quite as robust. In fact, I’d be willing to bet that next day is run by a completely different team.
We used to fairly often get 2 or 3 day delivery out here in the sticks (rural central Kansas). Nowadays I get stuff faster if I order it from eBay. Weird thing is, regularly Amazon doesn't ship my order for several days and then when it actually ships it only takes 2 days to get here.
My guess is that before the order shows as “shipped” in their website, the product is moving through Amazon’s internal logistics network. When to show as “shipped” is a somewhat arbitrary decision when the company runs a sprawling network that delivers to your door.
its probably not about distribution center, but how close you are to major warehouse where they stash popular stuff.