You are not alone. As I originally stated, I can get Bluetooth to work, it's just not as smooth as it was in IOS 9 or how it works with Android (at least for me). I know it's not my stereo because it works perfect with iOS 9 and also with Android. None of these issues popped up until iOS 10.I've had BT issues with both a 6 and 6s and my Garmin GPSs since OS10.
My 2011 Infiniti has tons of issues with iOS 9/10 Bluetooth but my 2010 chevy cobalt has 0 issues, I think it's just the software car manufacturers use and if it's not updated
I too had many Bluetooth problems after the iOS 10 update on my 6S Plus. I went through several full restores and set up as a new phone with each iOS update. The problems never went away. Mine would even lock up when trying to make a call on Bluetooth. Finally did a tech support chat with apple and they sent me a replacement phone. The new phone is flawless with Bluetooth. The funny thing was that my original 6S Plus was flawless on iOS 9 but never quite right once iOS 10 was installed. Maybe apple will replace your 7 Plus to fix your issues.
I too had many Bluetooth problems after the iOS 10 update on my 6S Plus. I went through several full restores and set up as a new phone with each iOS update. The problems never went away. Mine would even lock up when trying to make a call on Bluetooth. Finally did a tech support chat with apple and they sent me a replacement phone. The new phone is flawless with Bluetooth. The funny thing was that my original 6S Plus was flawless on iOS 9 but never quite right once iOS 10 was installed. Maybe apple will replace your 7 Plus to fix your issues.