The day will come when educators realize math and science are not disciplines that best describe the "real world."
Memorizing and being tested on both of them to achieve needed grades serves the societal purpose of advancing forward in a manner demanded by school systems. Don't let that serve as the final say to reality. You will fail if that is your belief.
I'd be guessing that if educators haven't yet discounted applied maths and physical science as describing the "real" world in 2,000 years, then it ain't never gonna happen.
"Memorising" and "testing" students on maths and science has
nothing to do at all with the already-qualified scientists working in the field. We—all of us—need to remember at least the basic principles and practices of maths and science if we're to study the world in real time and in real space. The science kids learn at high school is only one of the very first stepping stones to becoming a researcher, so I disagree that it's only to satisfy the school systems.
An research scientists certainly don't give a damn about the social implications of their work—other than that it's supportive of, or advantageous to, our society.
We look at a mountain, and trigonometry tells us how high it is without climbing it; we cross a river, and hydraulics tells us its flow rate without using a bucket; we cook a pizza, and thermodynamics tells us at what temperature without burning our hand.
Science and maths are inextricably tied in with the real world. Using your "real world" assessment for each of my examples could yield answers along the lines of "pretty high", "fast flowing", and "really hot". Which are more accurate? My answers or yours?