Hahaha, after years with Amazon Prime (from 2006) going back to a European country with no Prime was indeed quite annoying and I found it hard to explain to people what they were missing. Right now I am in the UK where there is prime, so I am again a subscriber although it is pricier and worse (way less stuff, higher prices, earlier cutoff for next day delivery) than the US.
Now, for me though, it was even more amazing than your description. It seems that it depends on where you live, but I was in NYC and I almost always got my stuff next day using free prime shipping. In fact, my wife ordered once a silver necklace at 2am before going to sleep, and at 9am, a mere 7 hours later a knock on the door woke us up. Sure enough, the necklace had arrived!
And that is not the only cool thing about it. I moved into a new house, went into amazon, the next day I had a projector, a projection screen (very heavy 120" with tripod), an home theater right at my doorstep. Free shipping. And a couple of months later my home theater amplifier had a problem and the manufacturer told me I had to ship it to their service (heavy amp, my own shipping cost), I wrote to Amazon asking whether they could help even if it was beyond the 1-month return window. They said they'd be happy to help and sent me a pre-paid return label, I sent it and got a full refund! Obviously, after that I bought all the big ticket items from Amazon. In fact, for computer parts I used to buy from NewEgg, but while their RMA was fast, you had to pay your own shipping back (also there was re-stocking fee IIRC on some items). But after having repeatedly excellent service from Amazon, I valued the fact that the item would arrive faster and would be shipped back free with a printable label if there was a problem for a full refund, so bought from Amazon even in cases where the price was somewhat higher.
Streaming is just an added bonus. The Prime experience was worth it before streaming and it was a real bargain at that price. Oh, some people complaining about bad experiences with Amazon, confuse Amazon with Amazon Marketplace - which is like ebay basically.