But, if you multiply "once in every ten thousand years" by all the different kinds of things that could be said to happen once every ten thousand years, don't you get something closer to "many times a day"?

The computation is not relevant, because when you make a prediction that, say, some excursion in the stock market will happen only once in ten thousand years, you are making a prediction about that specific thing, not ten thousand things. It will be a thing you have never seen, because if you had seen it happen, you could not claim it would only happen once in ten thousand years—the observation would be a refutation of that claim. Since you have not seen it, you are deriving it from a theory, and moreover a theory applied at an extreme it has never been tested at. For such a prediction to be reliable, you need to know that your theory actually grasps the basic mechanism of the phenomenon, so that the observations that you have been able to make justify placing confidence in its extremes. This is a very high bar to reach. Here are a few examples of theories where extremes turned out to differ from reality:

Newtonian gravity --> precession of Mercury

Ideal gas laws --> non-ideal gases

Daltonian atomic theory --> multiple isotopes of the same element