The problem is that professional mathematicians have a common language that they all have learned which serves them well...and they're the ones writing the Wikipedia articles. Imagine if all the programming documentation you worked with was at the level of a 1980's first book on BASIC.

Set theory is the concrete starting point after that training, and the first step of concrete problems is to translate them into an abstract form of maps on sets. It's a decoupling. Instead of translating n techniques into m domains (n*m bits of work), you develop n techniques in terms of set theory, and translate m domains into set theory (n+m bits of work).

Physics majors largely use the same pieces of math on the same domains, so this decoupling doesn't make sense for them. Similarly, most domains carve off some piece of math and statistics and specialize it. But if you're writing a reference, whose specialty do you choose?