Is there any way to make the phone ring when the headset is left on? My husband will take the earpiece out of his ear but leave it active. When a call comes in it rings in the earpiece and not through the phone. He hates the lag time it takes for the earpiece to connect if turned off but it also hurts to leave it in his ear. If the phone would just always ring, it wouldn't matter where the earpiece was.
I don't think that this is possible. If one has a Bluetooth headset connected with his iPhone, all audio will be played through the headset, not the iPhone. You can keep the devices paired and disconnected and that will save a lot of time when you switch to and from bluetooth headsets.
Since the software won't do what you hoped, an option would be to look into using a more comfortable or faster Bluetooth accessory or even choosing portable speakers as they often work well. Also, you might see if your phone supports Bluetooth LE (4.0) as the latency to connect drops from 100ms to 6 ms (which is how long the hardware takes to recognize a reconnect to a known device - as opposed to re-pairing two devices for the first time) to reduce the time it takes to transfer to the newer headsets.
Another option would be to get something like the Apple Watch so that you get notified of calls and alerts without needing to hear any sound and/or having the sound very close to your ears no matter what the iPhone has connected to it.