[SomeStupidPoint]

It's because you and the person you're replying to have the tail wagging the dog when it comes to being precise.

Powerful ideas are made precise, but they don't spring into being that way -- their inception is usually a fuzzy mess of analogy and hunch. Similarly, if we had an idea in mathematics that didn't fit in a formal system, we wouldn't just bin it, we'd change the formal system so we could implement it. (It's not like we have a formal system, or even a formal system we think implements all the things one should. Formalisms research is a major ongoing topic only ~200 years old.)

The precision and formality are the final product, but almost no ideas would be had if we required that they met our standards for formality when they were first conceived.

Creativity happens without being precise, and precision is usually a sign that the creative portion of the work has moved elsewhere.