That's surprising to me as a US customer. Unless I'm notified at checkout that something is out of stock, I fully expect Prime deliveries to arrive within two days of ordering. In fact, I've seen items that took an extra day to process get shipped overnight to make up the day.
The US Amazon checkout shows an estimated delivery date for Prime items that includes processing time and is >95% reliable in my experience.
Amazon prime is consistently next day in the UK (and I'll happily pay a non-trivial premium to order something on Prime) - even sometimes same day, although that's never promised, just an occasional nice surprise. GP is talking about "marketplace" which has wildly varying delivery time (a lot of the products are drop-shipped from China), but generally do arrive within the promised window.
The parent was talking about non-Prime, though, and they didn't claim the estimates weren't accurate.
My non-Prime sold-by-Amazon in-stock orders from Amazon US consistently take 3-6 business days to process but they still arrive by the estimated date (so it is fine by me). If I pay for faster shipping they ship on the day I order.
The US Amazon checkout shows an estimated delivery date for Prime items that includes processing time and is >95% reliable in my experience.