Your experience might be true in a big American city, but in Europe it's the complete opposite. Amazon is relatively fast (2 day shipping), but the grocery selection is limited and full of third parties charging extortionate prices. E.g. the same brand of nappies is 2x more expensive than getting it from Tesco. Anything specialty, such as musical instruments, PC parts, furniture, etc. is more expensive than getting it at the source, and all "cheap" items are 2x-5x more expensive than buying it from China, shipping included.
Amazon beats other shops in terms of convenience and selection (you can buy lots of random unrelated items and get them delivered fast), but often it's basically just a more upmarket eBay.
It's pretty great where I live in Europe in a country where they don't even operate. If I buy on Amazon.de, they ship products from Germany and items usually arrive within a week including going through customs, as they remove EU VAT and include local VAT at time of purchase (which probably clues you in to which country I live in). This avoids the massive customs processing fees, extra VAT, and wait times I would incur from most other international sellers.
Their prices are almost always the lowest I can find on books, similar to Book Depository which they also now apparently own. Other items like the small kitchen appliances I've bought on the DE site are also almost always cheaper than I can find in brick and mortar stores.
I'm not sure they have the same grocery service in most European markets that they have in the US, where as I understand it the grocery orders are handled rather separately with local selections.
Amazon beats other shops in terms of convenience and selection (you can buy lots of random unrelated items and get them delivered fast), but often it's basically just a more upmarket eBay.