There is one published paper that addresses the point about robotic probes and even suggests where to look for them
INFLATION-THEORY IMPLICATIONS FOR EXTRATERRESTRIAL VISITATION
J. Deardorff, B. Haisch, B. Maccabee and H.E. Puthoff
Journal of the British Interplanetary Society, Vol 58, pp. 43-50, 2005.
Generally, I think at least one obvious answer to the question in the op is this: If we have been or are one day visited, for better or for worse, it would be one of the most significant events in all of history. It is no wonder the idea fascinates people. And given the lack of definition and boundaries for such notions, esp for those without any scientific education, imaginations run wild virtually without limits. Hollywood helps provide a lot of fuel here, no doubt. But many of the UFO activists are the worst offenders. I have watched a fair number of people get into this and slowly develop more and more exotic beliefs as they fall victim to the nuttery surrounding the subject. Because of its potential significance, the idea of ET visitors can probably be as powerful as any religion.
I suggest that this thread has become far too speculative in regards to the what-ifs.