How can I set to show window switcher an all displays when I hit Cmd+Tab I two monitors plus my macbook display and I find it sometimes annoying to find where the window switcher shows up. It would make sense to show it everywhere when I hit Cmd+Tab. Please give me advise how to set my mac to behave that way.
Unfortunately, there is no such option available on Mac OS.

Nevertheless the application switcher always appears on the same screen on which the Dock is.

If you use OS X Yosemite or newer and have the option "Displays have seperate spaces" enabled in your system settings, you can move your mouse pointer all the way down to the bottom of one of your displays and the Dock will appear on this screen. This is the only way I know to select on which display the application switcher shows up.