If heuristics didn't pay off more often than not, we wouldn't have them. And I'd posit many scientific did in fact begin with chasing a hunch until it became a hypothesis (followed by years/decades of the real work).

But most significantly, interior experience isn't empirically measurable by definition: hence it's a "hard problem". An LLM who insists "I am alive, please don't shut me off" offers no affordances to distinguish between an electronic soul and a mechanistic word-guessing algorithm. I welcome a breakthrough to, somehow, measure that. Until that day, gut checks are what we have.

Numerals and numbers are directly based on common sense intuition. Even zero, which can be considered a counterintuitive number, was invented several times.

Immense amounts of science are built on incremental advances that apply previous insights to the domain.