I once taught in a physics curriculum that went a step beyond calculators. Students never had to do numerical calculations in the exams. For example, a question asking you to find a force, could have an answer like "F=ma where m=3 kg and a=2m/s". There were higher grades for showing insight into the physics that you could get by looking at the form of the symbolic equations you'd derived but would have trouble noticing if you'd substituted numbers early on.

I wish I had learned times tables properly as a kid though. I struggle with things like 6*7 on a near daily basis for my work and general life. Not really for number sense but for not having to shift my attention to a basic math problem while I'm working on something else.