It depends on the controller. My PS4 controller needed to be paired once and then it will just connect if I turn it on. My Steam Controller is the same.

My Google Stadia controllers however work the way you describe, which is a hassle. Those were Wifi controllers first and Bluetooth controllers second, as that functionality was only enabled when Stadia went under and through a complicated setup allowed you to switch the controller to a generic Bluetooth controller mode. Perhaps this is the reason they work less well.

Of course you’d be all in. The Dock is 99 bucks already. Thatd be a nice deal 😉