While my experience with Verizon pricing is that they can be a bit of a ripoff, my experience with their customer support has been a good one. They are consistently rated the best carrier for customer service, which isn't saying much, sadly. I've tried At&t and found them to be beyond clueless on a number of issues. I was with Tmobile back when they called themselves Voicestream. Bad. Nextel. Bad. My kids had Virgin Mobile which was Sprint PAYG at the time. Bad. I don't have personal experience with Sprint but the consensus I've heard is that they are the worst for customer service or possibly tied with At&t. So there is a teeny weeny itsy bitsy kernel of truth to Verizon saying they "support" iPhone 7 because I'm sure they put their call center people through training to help users with activation and other issues.
While I routinely call Apple for any issue, I don't dread calling Verizon like I used to dread calling At&t. One example is when I was in the line at customs trying to get international calling working at the Canadian border. The Verizon call center rep had it working before my phone lost contact with US towers after I cleared customs. I'm sure that with At&t I would have never gotten through to the right person and I would have simply had to give up on data and switch to Airplane Mode to avoid getting reamed for ten dollars a kilobyte (or whatever).
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All iPhones have the radios they need for all networks. There is no difference in the "sim free" phone versus the one you are able to pre-order today other than the one you get now requires you to have an account at a US carrier to order the phone. I'm pretty sure if you pop open the sim tray you will see a generic Apple SIM that could easily be activated for any carrier. I was surprised to see the procedure for taking an At&t phone to Verizon was to simply pop in a Verizon SIM. So I had an At&t iPhone 6 that had never seen CDMA in its life suddenly working on Verizon LTE and downshifting to Verizon 3G (which is CDMA) if it needed to. To me this is evidence the radios in the iPhone support all carriers, otherwise Apple would be selling dozens of models. I think they only sell one model of every phone and association with a particular carrier is something that is handled by the SIM card and the network.
When I first tried taking my phone to Verizon, the Verizon store put in their SIM and it didn't work. I then found that I had one payment to go on my At&t iPhone purchase so I paid it and asked At&t to unlock my iPhone 6. I was expecting to get an email telling me to connect the phone to iTunes or some other nonsense. In fact the unlocking happened over the air. I returned to the Verizon store and they put their SIM in and it worked right away. There is another barrier to putting in a new SIM and that's "find my iPhone". You have to switch off "find my iPhone" before switching SIMs. I believe it's still possible to switch SIMs but it would require you to log in to iCloud to use the phone with the new SIM while (temporarily) turning off "find my iPhone" before putting in the new SIM would allow you to simply start talking right away.