As I understand it bluetooth is used for iBeacons & other similar services with location services…
About iBeacon on your iPhone, iPad, and iPod touch - Apple Support
Turning it on when indoors can help if you are in an area that may be in Apples databases (like shopping malls and other public spaces).
Obviously other services should work before bluetooth is involved (cell towers & wifi should be easier to get a fix as they should be more abundant).
Other things I would try…
Reboot all devices.
Reset the network settings on iOS (you will lose any remembered wifi networks).
I'm afraid after that my temptation would be to backup and restore the device in iTunes. I have to wonder if iOS 10/ macOS Sierra has somehow synced a 'location services are off' setting across the devices. My instinct would be to test without syncing to iCloud then restore a backup & see if it comes back.
Use an iTunes encrypted backup to keep all your saved passwords. iCloud backups can also work, but can take longer to restore.