While I agree with your statement in general, the reality is that you can't conduct science this way in every field. Physics, microbiology, sure. But what about humans? You can't cage humans and control every little bit about their environments except for the single thing being studied.
If you don't have falsifiable theories, you don't have science. "Social science" isn't a science. "Economic science" isn't a science. As a rule of thumb, if a discipline has "science" in its name, it's not a science.
So, the definition of science needs to be flexible enough to include these other methods and I think the phrase "systematic methodology based on evidence" is appropriate.
Not everything has to be a science.
Cosmology and theoretical physics is full of concepts that we haven't been able to formally test yet, but I think most folks would still include that labor under the umbrella of "science".
Because they make predictions that can be disproved. They can be wrong.
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