I would seriously choose creating own scripts for canvas components, then aplying canvas public methods to all children, p...

You can use either, that’s why it’s built that way. They're event systems that you use to call other methods when something happens on that UI element.  Also adding all your UI based methods in one class is perfectly fine. If you plan on reusing a lot of UI methods in other ways then creating a stand alone script would be ideal, in this case we are not doing that.