airports with up to a million passenger movements per year can operate without any air traffic control and without even a UNICOM operator?
Number of pax per year is irrelevant in dictating the level of ATS. That's just scare tactics to the public who don't know any better.
The level of ATS & airspace classification is dictated by traffic levels. And even the FAA don't consider UNICOMs in determining the level of ATS required at a particular AD.
What would happen if your radio stopped transmitting when you were making the recommended broadcast? How would you know?
And how would the Tower - and least of all a UNICOM operator - know who's responsible? A dead carrier could be coming from anywhere, if there is one at all. Radar surveillance would (and does) detect unidentified traffic and is passed as part of RAS if it is relevant.