Yes, it does. The added discounts, added features (free video streaming, free MP3s from time to time, free 2-day shipping, occasional free ebooks), and convenience more than make up for the membership cost.
It's irrational not to use Amazon when you're a Prime member.
Well, for the most part, my expenditure on Prime is usually justified within weeks after I renew it. I work from home, in the suburbs, and do quite a bit of my shopping online.
I have, within the past month or so, bought inner tubes for my bike, other bicycle accessories for the new bike I just bought (pump, water cage, water bottle, wedge pack), a pair of boots, a new Aeropress, one paperback (for the daugher) and a smattering of Kindle books.
I don't shop just to justify the sunk cost, but it should probably go without saying that while some (or none) of those purchases may not have been the very best price I could have found them for, they were all priced reasonably, and I suspect, well below what I would have found them for at the nearby brick and mortars, without having had to leave the house for it.
That said, ignoring the 'sunk cost fallacy', as the chances of finding 'better-than-Amazon' prices locally are slim to none, I am an idiot if I don't buy from Amazon wherever it makes sense to. Obviously, packs of deodorant and shampoo are borderline, but free shipping on a lawn mower that's half the cost of Home Depot? Ideal use of Prime membership. Not exercising it means paying more, and going through considerably greater effort to do so (lugging the box around, borrowing an appropriate vehicle to carry a lawn mower, etc.)
Not sure why you're getting downvoted, as from a purely economic standpoint that is exactly right. I think the point other people are trying to make is that given you have already subscribed to Prime, things you would already have purchased are now available for less via Amazon.