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Common core math is how high performers in math tend to already approach math concepts. The controversial examples focused on "number sense" do instill good habits and instincts for error correction (especially important in the age of calculators and computers), and don't detract from the importance of the actual mathematical operations. Either way, common core math curriculum as a whole is good, and continues to be a good set of goals for learning math. I'm somewhat sympathetic to the argument that the math standards are too high and leave some kids behind, but that's less a problem with the standard and more a problem with our ability to get kids up to that perfectly reasonable standard, of what we should hope that all adults should know.
The main criticisms of common core that I sympathize with are that they deemphasize the humanities too much, but that's not exactly a problem with the math standards themselves.
My only real exposure is helping friends kids with their homework, and it really seemed like they were focused way more on shortcuts to correct answers for simple problems than how and why numbers interact. Which I guess is kinda what you're saying! Imo those are great techniques for working at a higher level, but in no way a substitute for observing and understanding the processes that lead to those answers. You'll get plenty of competent accountants that way, but you won't inspire many mathematicians.