None of the big 4 U.S. carriers are going to require you to pay for your phone completely up front.
Even if they did, they could always use their Visa. No, that's Declined. Perhaps American Express? Haha1
Yes, people will still make a down payment and monthly payments, however, now the price of the phone will be "known" to the consumer. Whereas before, it was just, "Oh, you're on a contract. You can have this phone for $1 (or $99, or whatever)." The sheer number of people that didn't realize they were actually for it with their contract is ludicrous.
Now people will see, "Oh, I'm paying $99, plus $59 per month for 2 years? Really?" It won't stop everyone from buying, but there are some people out there that will now say, "Okay, I'm going to shop around and see what I can find. It might be cheaper in the long run to pay one out on my Visa card at a 3rd party retailer, because will also double my warranty." Amazon.com, Best Buy, and others may see a slight uptick in phone sales from it in the long term.
The Lumia 635 GoPhone was available for $49 at Walmart and on Amazon. At AT&T, the same GoPhone was $99.99. Why? Because AT&T needs to pay their store employees, etc. I learned from a Walmart manager that their cost on the 635 GoPhone was actually $35, so they made just under $15 per phone. Considering they don't have to train employees to help customers with the phones that they sell, they have a much lower overhead. I think a lot more people, when they realize they can save $25 per month purchasing a phone outright may start to consider less costly alternatives. By a lot more, I don't mean a majority, simply a lot more people than do now, simply because their eyes will be opened.
When I explained how it all works to my Father-in-law, he and my mother-in-law went out and purchased no-contract phones on the spot, and they haven't been on contract since. He won't buy phone insurance either. "I pay less than $50 for a new phone, so why should I pay monthly for insurance that requires a $50 deductible when I can buy a new phone for the $50." He's right, too, at least for him.