The exact same thing happened to me. My iPhone 7+ worked fine the first day, but no service when I woke up the next day. I tried re-inserting the SIM card, resetting network settings and a full erase, but no luck. When i put the SIM in my iPhone 6, I get service just fine. Also tested the SIM from my wife's iPhone 7 and got no signal in my 7+ as well.
I called AT&T and they confirmed my SIM is good and they believe it is a hardware issue (or an Apple issue) and transferred me to Applecare, which they believe it is a hardware issue and set up an appointment for me with the local Apple Store. The Apple Store ordered a replacement for me, but they have no idea when they will get one. So for now, I have my SIM in my old iPhone 6 and my 7+ sits powered off in a drawer. The lady at the store was nice and understanding, but it's still a bit frustrating.
Hopefully the replacement doesn't have this issue. No idea if it is an iOS bug or truly defective hardware. I've seen this bug being reported by several people on forums, etc. but it's obviously not that widespread or we'd be hearing a lot more about it. Best of luck!