I think more people have this problem than you realize. They have just learned to deal with it or ignore the issue.
Here's my experience with my iPhone SE. I have the same issues most of the other people here are describing. I'll be connected to a bluetooth device such as my car's handsfree or a bluetooth head set (I've had two different brands Jabra and Plantronics), they will randomly disconnect and switch back to the "iPhone" audio output selection while I'm on an active call.
Also if I'm playing music to my car via bluetooth it will sometimes disconnect. I notice this happened probably 80% of the time when I'm leaving my house and I have music streaming via bluetooth. It would disconnect as I was driving away from the house, maybe about 40-50 feet away from my house. So I started trying a few things to try to narrow down what was happening. I speculated it had something to do with leaving an area where I was connected to WiFi. This also was true with the headsets disconnecting as I was leaving work. I turned off the WiFi radio and I would say that cleared up 90% of the issues I saw.
So after discovering this, I took my phone in to the Apple store. I described what I was seeing and they gave me a new phone. The new phone did the exact same thing as the old one.
Long story short I believe that they have a fundamental design issue where the bluetooth and WiFi radio are a shared radio and when a "disconnect from WiFi" event occurs, that has some impact on any bluetooth connection that may be established. I can't confirm this theory so I guess I'll have to leave it as my opinion.