The hiding mute button also really bugs me - given that it something you generally need to have quickly accessible during a meeting, it really should be always visible & on the same spot. BlueJeans has this right - the button is always acesible and not moving around.

As for keyboard shortcuts - unless they are global, they will not work well if they need window focus as that means you still need to find the browser window in which it is running with your cursor and might as well click a button.