I think only mouse-1 should not popup menus, but in many modern
applications mouse-3 is a standard way to show a popup menu
with a complete list of items related to the main item invoked
via mouse-1.
I don't recall an application offering a menu on mouse-3 specific to a
certain tool bar button. E.g. Firefox 1.5 displays the same as <Menu>
<View> <Toolbars> does, no matter at which tool bar position you click
<mouse-3>.
What I meant is that in Firefox [mouse-3] on a tab pops up a menu of
tab-related actions other than activating a tab as [mouse-1] does.
Also [mouse-3] on a link pops up a menu of link-related actions,
on an image - a menu of image-related actions and so on. Emacs could do
the same for the toolbar icons. Even in Firefox [mouse-3] on the [Back]
toolbar button displays a list of all previous nodes.