I will add, when I say "forget" doesn't forget a device, the iPhone may well forget it but the Bluetooth device you were previously connected to doesn't forget your iPhone and it keeps pinging it, causing stuttering. In my case it was a Logitech Bluetooth adaptor and after posting the details here, I helped a couple of people resolve their stuttering issue who had the exact same Logitech Bluetooth adaptor as me. I guarantee most if not all the people with the issue here stems from the same underlying issue, whether it be a Logitech adaptor or some other device which keeps pinging the phone. You can resolve the issue by getting a new phone, but as soon as you connect via Bluetooth with the new phone to the device causing the issue, the same thing will happen no matter how many new phones you get. You can only resolve the issue by finding whatever device is causing the issue, whether it is a Bluetooth speaker, watch, toothbrush, whatever.