Issues turning on the Roku Ultra

The power button doesn't turn the Roku "on" because it's never actually off. The Roku is always on if it has power. It simply drops into a low power state when it's not in use. The power button is solely to control your TV. Yes, the Power Saver function is glitchy, so it is recommended to turn it off. The Roku uses very little power anyway, so any power savings would be measured in pennies. 

When you press the Home button on the Roku remote and the TV turns on, this is something called CEC (Consumer Electronic Control) and there's nothing wrong with using that function. In fact I use it all the time. It will turn the TV on and change the TV input to the HDMI port the Roku is using. It also allows the Roku remote to control the TV volume. If you have an AVR in between the Roku and TV, CEC will also turn the AVR on and change its input port as well. If you're watching OTA TV and want to switch to the Roku, just pressing the Roku remote Home button will switch it over automatically.