I'm not clear that "in a recession" is a particularly useful state to anyone.

Even with a complex formula, you're still dropping the useful details.

Even with a predictable complicated formula, you still have the question to debate: "does it matter?"

People like certainty more than uncertainty, even if it's a bad certainty. That's why the have all these classifiers. It's easier to handle two situations "we're in a recession, we're not in a recession" than track about 50 economic parameters that are interwoven in a thousand complex ways. If you are a professional economist, you probably need to do the latter, but if you are a regular person, you probably have neither time nor capability to do it.