When I do shop elsewhere, I don't mind entering payment details as long as I'm not required to save them (I don't trust most sites not to be hacked and leak my payment details). But if I ever get a delivery time over a week or a 'back ordered' status, I cancel the order immediately, because I know that they don't really have the item on hand and are just gambling that they can broker the sale at a profit. I've had merchants outright admit that they can't fulfill an order unless they can add some high margin accessories to an order. Not a game I'm interested in playing.
At a random online shop: are they trustworthy? do they really deliver on time? Are those reviews legit? etc. etc. Before I deal with that, I just order from Amazon. Convinience.
And yes, once you are in prime, you are even more bound and inclined to it.