My wife and I both have iPhone 7 128GB Verizon. Mine is Jet Black and hers is Silver.
My phone has been dropping to "No Service" as described on this forum. My wife's phone, on the other hand, has not been dropping to "No Service", however every once in a while has been going to 3G / 1x. This has been annoying but nowhere near as frustrating as the No Service issue. So not all Verizon iPhone 7 phones are experiencing the No Service issue.
I went in to the Genius Bar and they are replacing my device. The tech also noticed that my phone was very hot (I had noticed it too after I unboxed it but thought it was a normal iPhone 7 thing).
My theory is that there are two issues: 1) the No Service issue is a result of bad hardware (antenna or something), but 2) that there's also an issue with Verizon (the 3G / 1x thing) that is confusing things.