What makes you say this? As I understand it, we've only detected a tiny fraction of the planets out there and it could be that there are plenty of systems out there similar to ours, we're just not capable of seeing them yet. Is there some reason to believe we're unlikely to ever see another system like ours, other than the fact that we haven't yet?
About half of nearby stars that we can observe[0] have planetary make up that is different than our own Sun. By definition, the rest either have a make up that is like our own or not like our own. So let's assume that every single nearby solar system looks exactly like our solar system, we are just unable to detect that they are at this time. That still means that our solar system is distinctly different than half of the other solar systems. That ratio of difference will never go lower, it'll always be "The solar system is different than at least 50% of other nearby solar systems". But after we do more observations, it might be 60%, 70%, 80%, etc.
Or in other words, as the original commenter said, "It is certainly possible that the more we study the rarer it will become. (It can't really go the other direction at this point.)".
[0] - FTA, "Of order half of nearby stars have at least one (and often several) worlds with masses substantially greater than Earth and orbital periods ranging from mere days to weeks; in our system, the space interior to tiny Mercury’s 88-day orbit is entirely empty."
Based on the best available scientific tools at the time, we once thought that the solar system rotated around the earth.
Based on the best scientific tools available today, we believe that our solar system and planet is extremely unique.
I think we don’t know nearly enough to say with any real confidence what solar systems outside of ours look like at this point.
It is true that we are ignorant of many things. It is not true that our ignorance is infinitely unbounded, and it is a denial of science and rationality, not an affirmation of it, to believe such. We have gathered enough data that we already know that our solar system is not perfectly pedestrian, and no amount of additional data short of the outright falsification of our current data (which, bear in mind, is a bigger ask than a falsification of a theory, which isn't much of an ask at all) can make it more pedestrian; it can only reveal more ways in which it is not normal.
Well, if you define our ignorance as information we don't yet have. Then if the Universe is infinite, it means our ignorance is unbounded.
In fact, if any type of infinity exists, then it means in general our ignorance is unbounded, because we will never be able to have full knowledge of that infinity.
For example, you can make as many assumptions as you want about the properties of the rational numbers in between two other numbers, but unless you are able to somehow "know" all of those numbers, then your ignorance about them is in part bounded by their quantity, and if it there's an infinite amount of them, your ignorance about them will be unbounded.