Created attachment 157965 [details]
A sample app that demonstrates the problem

When a QToolButton that has an empty menu is displayed, it will show a standard button with a dropdown arrow; however, when this arrow is clicked, a 1px by 1px menu is displayed, which is not expected.

Similarly, a QToolButton with no menu set allows you to click the dropdown arrow, but nothing happens when the arrow is clicked.

I would propose that in both of these scenarios, the dropdown arrow should be made unclickable and drawn in the disabled style.

See the attached main.cpp for an example of this behavior.