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. Clinical trials are good, but there are many things which can't be practically studied this way because of the cost, the follow up time involved, or even the ethics.

Therefore, we must rely on scientific methods that fall short of the gold standard of the "experiment" (or in the case of people, randomized, double-blind, placebo-controlled clinical trials). 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.

Besides, science also includes the process of building up observations, knowledge, and understanding that leads to more formal experiments. That process may be systematic and involve evidence but hasn't yet reached the stage of any sort of experiment. 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".