> Who cares anyway?

I can’t tell if you’re just joking. Proofs of facts that seem obvious or irrelevant are very important not for the yes-no question they answer but for the development of the deep mathematical theory they necessitate.

It's not that mind-boggling. In general we need to use specific properties of numbers to prove whether they are irrational, and pi+e has very few useful properties to work from. Even proving pi is irrational is not trivial and it is one of the transcendental numbers we know the most about.