Start update-process by clicking on application taskbar button or desktop shortcut

It is almost unbelievable that updates are allowed from the Start Menu but not from the (infinitely more used) Desktop shortcuts and taskbar buttons. I'm saying this neutrally, as in: "if you told me something like this would happen, I wouldn't believe it."

As said above, there are business apps in play here and sometimes time-critical updates. 
This is not only technology which we've always had before (e.g. ClickOnce), but also very basic one.
There is absolutely no theoretical justification for omitting updates for shortctuts and the taskbar, or even for splitting the update process in two, leaving one use case (ironically, the much preferred one) in complete darkness regarding one's application's updating.

Also, asking users to start the application, then close it and then start it again to check if the update went fine is very counter-intuitive and unprofessional.