Now fast forward about a year and a half later, Apple has announced that they will be repairing affected devices for free (via MacRumors). According to Apple, “Apple has determined that a small percentage of iPhone 7 devices may show “No Service” in the status bar (even if cellular coverage is available), due to a component that has failed on the main logic board.”
“These affected units were manufactured between September 2016 and February 2018 and sold in China, Hong Kong, Japan, Macao, and the U.S. If your device exhibits the symptom described above, Apple will repair your device, free of charge. Your iPhone will be examined prior to any service to verify that it is eligible for this program. This program only applies to iPhone 7.”
The model numbers affected include A1660, A1780, and A1779, which as Apple mentions above seems to affect units sold in the US, China, Hong Kong, Japan, and Macao. You can check for the model number on the back of your iPhone towards the bottom part of the device. If you have one of the affected models, then you can send your device in for a free repair.