There are significant bluetooth bugs for the AT&T model 7/7+,
Got to be careful with saying "AT&T model 7/7+"… again, it is the Intel-radio A1778/A1784 models that are the "Apple supported" models on AT&T and T-Mobile. HOWEVER! Depending on where the user got the iPhone, they COULD have gotten a Qualcomm-radio A1660/A1661! Best Buy, Target, etc are giving the Qualcomm-radio iPhone out for everyone, regardless of carrier. This could be why some "AT&T customers" aren't seeing the Bluetooth problems… they might not have an Intel-radio "AT&T" iPhone. At this point I have seen no reports that ties the Bluetooth quality issues to AT&T LTE frequencies (although I have seen users report disabling LTE helps/resolves) regardless of radio manufacturer; only reports that states the issue ties to the Intel radio.
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PLZ APPLE, FIX THE GOD DAMN bluetooth issue that causing no messages notifications to come when you have the screen off and BT ON !
Where are you seeing this behavior, please be specific.
I have filed nearly a half-dozen bugs with Apple on Bluetooth headset Notification sound "capture" issues in the past two years, specifically wrt iOS capturing A2DP/AVRCP devices as the default "AirPlay" output device and dragging Notification sounds along with it. Apple and I have a significant difference of opinion on whether this should be "default behavior". Thus far, I have not "won". I'm glad to see it is annoying others… perhaps we're on the way to getting it fixed. It certainly does NOT "works as intended" for anyone I've met who uses Bluetooth headsets; not sure who Apple is talking to. It only happens to A2DP/AVRCP devices, not HSP/HFP devices… as far as I can tell. [Apple never answers my question of what EXACTLY is their INTENDED Bluetooth behavior. They like to keep us guessing, I suppose.]
In my testing so far with iOS 10.1.1:
•iOS is playing keyboard "click" sounds through the Bluetooth device when "captured" (REALLY? can you eat a headset's battery any faster?)
•Some (perhaps all?) Bluetooth car audio systems cause iOS to switch from a Bluetooth headset to the car audio system when the car is turned on, EVEN IN THE MIDDLE OF A CALL, regardless of the Accessibility:Call Audio Routing setting; this clearly should NOT be intended behavior, as most headset audio quality is significantly better than just about any car audio speakerphones (Maybe with the exception of Tesla… theirs is pretty nice. But… Then again, would explain Apple's moronic choice here, if anyone has ever seen the parking lots at 1 Infinite Loop.)
•iOS will automagically connect to some Bluetooth car audio systems—I know some VW—if paired, even if the car audio system does not have the Bluetooth audio set as "active". This basically means audio is captured from the iPhone and sent into a blackhole in the car audio system, including Notification sounds and navigation.
I can report that Apple has seemingly resolved Call Audio Routing issues with Phone, FaceTime and FaceTime Audio in iOS 10.1.1 and 10.2. Between iOS 9, 9.1, 9.2, 9.3, and 10.0, Apple played a comical game of Regression-pede, where various incarnations of answering calls would not make it to a Bluetooth headset. Infuriating for hearing impaired users like myself. I imagine, as Bluetooth devices proliferate, thanks to hands-free laws and car makers finally getting up with the times, as well as Apple jumping into the market with AirPods and BeatsX, we're going to see the frustration level start to rise with the "common folk" as it has been with the hearing impaired and headset users for nearly 5 years. Apple has just been out to lunch on it.