In the secretary problem, we assume that your ability to distinguish a good secretary from a bad one is fully developed from the beginning. In the examples given, you spent a significant amount of time (maybe even your whole life) figuring out what makes a good partner, apartment, or job. It's a neat problem, but I would be concerned for anyone who uses it as a life guide.

My favorite math problem that offers a realistic solution to a practical problem is Sperner's Lemma (implemented here [1])

[1] https://www.nytimes.com/interactive/2014/science/rent-divisi...