> The issue is, as I pointed out, that it works for anything

If you find it used "for anything" you can point to such cases where it is improperly used. When it is used for the case where we genuinely don't have enough information to claim any "probability" then it is simply a more colorful statement of that fact: that there is really nothing actually measured and known based on which any other statement than "we know exactly one example that such outcome is possible because we live in this outcome" is honestly impossible.

You may psychologically not like that fact, but when there is no more data, it has to be admitted that there is no more data to claim anything else than that. Maybe the following can help you: Imagine you find yourself in the middle of the desert, in all directions you see only sand. People today know that every desert ends somewhere, but that's based on the fact that enough people don't live in the middle of the desert, so you must imagine that you are the very first person that ever existed and that you find yourself in the middle of the desert. While moving around the place, looking for any signs, you may or may not find the proofs about something else in the distance. But you can genuinely be in the phase where you see only sand and can't conclude anything about the existence of, for example, the rivers or the sees.

The way I see it, the message is not "give up any attempt to learn more about the Universe you are in" the message should be "sitting around and inventing stories doesn't help: you have to move and actively search to find out more." The humanity was for a while good in inventing stories that sounded comforting but were completely unsupported, but we have actually in the last 100 years found the exact and provable signs about much more of our Universe than ever in our history: think about it: 100 years ago nobody knew that there exists anything more than one galaxy: ours. Today we can actually claim that there are one hundred billion galaxies in our Universe. And that most of them move away from ours. And we can calculate very precisely when all of them were on "one place": around 13.8 billion years ago. I'm always so glad that I live in this point of history to be even able to learn about that.(1)

If you want more answers, support the science which looks for the answers -- there have to be serious investments in the real experiments for finding out more because easily reachable information is already found. And the humanity sadly invests more in military equipment than in science. And a lot of what we've learned we have learned from the projects that are less "sexy": you don't have to have many humans walking on the moon to learn more about the moon, for example: using robotic probes is all that we need today.

But you should also not realistically expect the answers that are behind the limits of what's reachable for us. In the example of the first human in the desert, he can reach some land behind the desert, but being just a first human, walking there, he surely won't walk on the moon. He can however look at the moon and the changes in the shades from the sun on different places on the Earth and develop the idea that the Earth is also round. And that's how scientific discovery works: carefully doing enough experiments to be able to conclude something that was before unknown.

1) to reestablish the perspective for the day-to-day events, search for "Everything Is Amazing And Nobody Is Happy"