Microsoft (or a trusted 3rd party, the user can select a different provider) maintains an online database of trusted application vendors. Signed and trusted applications can do things that require a UAC popup without causing the popup to appear.
And who decides what constitutes a "trusted" application? How many third parties do I have to pay to have my application tested for approval? What happens every time it gets patched? What happens when the mechanism gets compromised?
Back doors are always poor security tools.