Switching ps4 controller between iPhone and IPad

I have a ps4 controller , which I want to use with both IPhone and IPad. The problem is if last time I used it with IPhone and now want to connect to IPad , I’ll have to forget the device in IPad settings and discover it and then I’ll be able to connect. And vice versa. If last time I used it with IPad and want to switch back to IPhone, I will have to forget it on IPhone and discover it and then it will connect. It’s pretty annoying. Why can’t I just switch the devices smoothly like with iPods or bluetooth speaker? P.S. I do turn off BT on the last device before connecting to the other one, so I am not trying to connect to two ios devices at the same time.