1. If you want rechargeable batteries, not disposable batteries, you will have to go broke, because the gamepad does not have a built-in battery. Fortunately, the GP has a set of a charger and four batteries for about 1100-1500. (for example, the choice is yours).
2. The controller has a headphone jack, but it does not work with Apple TV. Well, okay.
3. At first there were glitches. After using the gamepad, the Apple TV remote often did not work properly: either the sensor did not work everywhere (for example, in multitasking mode), or some keys did not work. It was "treated" either by sending the set-top box to sleep mode, or by rebooting it. But after the tvOS ates, a lot seems to have been fixed, I no longer notice those glitches.
4. Gamepad does not work with all tvOS features. For example, it does not rewind videos in YouTube. The functionality varies from application to application: either it does not work at all, or it works partially, or it works within the limits set by the application / game. Yes, in some applications, even basic functions do not work or work very badly, for example, banal navigation through the menu. So the gamepad will not replace the remote control. For now, at least.