We have the data to analyze the probability of a solar system like ours now. The observational limitations can be accounted for, both because we can understand

We have the data to analyze the probability of a solar system like ours now. The observational limitations can be accounted for, both because we can understand what our solar system would look like at a distance, and there's enough other data from systems that don't match ours to be statistically significant. The answer is that our solar system is exceedingly improbable. It is a top spinning stably for billions of years at a time, despite the general shape of it wanting to "fall down". It has several special characteristics in the shape of the outer planets that allow it to support what is in fact a very improbable situation with what we call the "terrestrial" planets being able to stay in the liquid-water zone for billions of years at a time. This turns out to be very abnormal. It is "improbable"; it is not "inexplicable". There are a number of good and interesting computer simulations explaining how our solar system can come about. However, it is definitely unusual. It turns out that there are indeed a lot of planets in the galaxy, however, the vast, vast majority of planetary systems end up completely unsuitable for life, visible even at the range we are at now. There's a few buckets they fall into, none of which look like our solar system. The Copernican principle actually died with exoplanet research. It had a good run, but it turns out that, yes, our Solar System is in fact quite improbable and unusual, and the Milky Way is also improbable and unusual, with its very unusually-quiet central black hole not blasting the entire galaxy with life-ending radiation as is the case with almost all known galaxies. In general most of the galaxies in the universe have vastly, vastly more radiation than the Milky Way. We may not be in the center of our solar system, but it turns out the solar system itself is special, and the galaxy we are in is special.