Nah it isn't ideal, I wanted to make a post about it eventually but I wanted to try some third party docks and/or see if updates fixed it.
What I have figured out is that the best way to use the dock is to boot the steam deck up not connected to the dock, get it to the home screen and then connect it to the dock. I find this has the best chance of inititating everything right.
Make sure to check the controller order under the control settings for a particular game, use change who is the number 1 control input easily once you learn where it is, and that can help some of the problems that arise.
I don't have any performance issues, but not that if you try to run a really high resolution tv at anywhere near a native resolution the steam deck just is going to quickly be outclassed by the performance demands. So idk, 720p sounds suspiciously low though, try checking the settings (under the lefthand bar) and examining how the display settings are set. Change it to native or some other setting and see if that helps, it might be that the settings are keeping your steam deck from jumping up to a higher resolution. Same thing with framerate lock, which you can check under the righthand bar, I recommend setting framelock settings (maximum framerate) on a pergame basis.