I'm not sure the workout analogy really helps. Our body is really good at optimizing movements you do often enough. Do enough push ups, at some point you will become very good at pushing things, do not expect to be good at pulling though. Run 1 km everyday and you will become a great short distance runner, try to run a marathon and you will miserably fail to finish it. Sure, you will get cardio benefits and get healthier overall for the first months, but once the newbie gains stop, training specific skills won't generalize to general ones.

Does education work in a similar fashion? does being very good at solving very specific timed algorithm problems at a whiteboard translate to being a good software engineer overall? If that's all you trained for, you will be just very good at that.