Self replicating Von Neumann probes could handle the issue of exploring such a large number of solar systems by increasing their numbers exponentially. They could leave behind machines that could continuously monitor and survey planets for millions of years.
If aliens exist, then I would expect for them to have observed us like that. Unless they have no interest in the outside world at all, which seems unlikely.
and the fact that so many people believe it to be utterly ridiculous that alien life forms could be exploring the galaxy, yet here we humans are, doing exactly that, is just completely mind-boggling to me.
The fact that they haven't suggests that either they don't exist or that they haven't found us.
Well I do wonder how friendly they are, given that they haven't intervened at all in Earth's history. I find that very unlikely. Moral aliens would probably want to help us, amoral ones kill us like you said. But the probability of aliens existing yet being indifferent seems unlikely.
You can even abstract out distance. I'm pretty sure there's some hierarchical struggle going on with the squirrels in my front yard, but I'm also pretty sure I don't care. And we're fellow mammals competing for the same nut trees and fruit bushes. If there are Star Trek Hortas tunneling under my backyard, I really don't care as long as they stay out of my basement.
Even within our own species there's a pretty strong taboo against colonialism that seems to automagically form right after (inevitable?) failed early experiments with colonialism. The odds of white people running Africa again are pretty low, even though we obviously did a better job than they are doing. Despite being incredibly easy to reach and staggering power imbalance, the colonies in Africa didn't last long and even a fairly irrational space alien would see the futility in trying to take over Earth.
There are many reasons to invade Canada. Stealing their resources of spar and mast grade timber for 1800s era sailing ships would be a pretty stupid idea in the current year. Its possible there's a natural magic filter such that being able to travel interstellar and having enough power to turn earth into a colony naturally means there are no material resources on earth worth the taking... What would a galaxy wide empire do with titanium, silicon based semiconductor electronics, or rocket engines, only miserable savages a million levels beneath them use stuff like that. It would be like handing a modern american a flint spear tip, what good is that other than in a museum?
http://diglib1.amnh.org/articles/kls/
Samuel Clemens aka Mark Twain did a good job illuminating how people tended to think this way, all the while forgetting that the people under a heavy thumb might not agree! Some things may have been better organized when white people were in power, but the German concentration camps of World War II were also "better run" by some definitions than a bickering gaggle of democratically elected disagreeing men in nearby European countries, and I don't think we'd really use them as an example of better run. I grew up partially in Nigeria, the target of many jokes, and no matter what issues they have there I know that many Nigerians who would never wish for a return to British rule.
1st) Freedom or self determination or at least less control over their lives by people far away
2nd) Racism (people want their leaders the same color as they are)
A distant 3rd) Measurable statistical demographic numbers for quality of life, like disease rates, death rates, crime rates, economic activity, education levels, etc.
I would propose this priority list is human, cross cultural, doesn't matter if its Rhodesia, Haiti, India, Korea, people naturally seem to come up with this sort order no matter the culture.
I think if we had super advanced technology and AI, we would do more. And certainly if we found other intelligent beings that were like us. We would probably do what we could to share technology with them. Or at least medicine and food.
I do doubt aliens would want resources. They might want our solar system to colonize with their own kind though. If they have population growth, then that is a serious issue. Or to build dyson spheres and computers out of our solar system. Or they might want to eliminate us because we could grow into a threat in the future. Etc.
There is little reason to not interact with us unless they are totally indifferent to the outside world.