As a military technical instructor for aircraft, you need both to accumulate common sense and troubleshoot a system. While classroom learning can help establish the basics. It is not sufficient to yield expertise. I've known people who understood a concept at a collegiate level who were totally at a loss when it came to practical application. My job was to take them from the basics, to full competence. I found it was much easier to train someone who already had a hands on common sense practical understanding of how similar things basically worked. In other words, It is easier to grasp technical concepts when one knows one end of a tool from the other. You can describe the biology, environment, diet, etc. of a fish and fishing in a classroom and that is not going to be very effective in teaching them how to fish. However, if you take them fishing, then introduce the relative concepts, they can gain a deeper common sense understanding and with practice, become an innovator or professional. Or you can teach someone the rules of the road from a state drivers manual, yet that alone is not going to transform them into an Indy or NASCAR driver no matter how long they sit behind a desk rather than sitting behind a steering wheel. For one thing, if they are hopelessly incompetent with the co-ordination of shifting gears, have a slow reaction time, and poor situational awareness, they can sit through all of the classes they want and still not even be capable of parallel parking or backing up while towing a trailer. So any additional formal education is an utter waste of resources. I worked on multi-million dollar military aircraft designed by college-educated engineers and yet found many design factors which defied common sense with alarming frequency. Leaving one pondering to oneself why on Earth they did something in "that" way, when common sense says it would have been more effective had they done it another way.
Generally, people who are good at "book learning" have less practical knowledge, or common sense. Is this the fault of formal education? No. It's simply a difference in aptitudes. Common sense can be developed through real-world experience, just like book knowledge can be gained through formal education, and it's the individual's responsibility to develop both.
Formal education helps one learn basic facts of life for the most part, and it can help make eon's understanding of the world better. This can help one increase their common sense and make better decisions as a whole.
For the most part, common sense is really quite a different story from what one learns in school. It's the difference between street smarts and book smarts, and they're a horse of a different color from one another.
Formal education in and of it self doesn't impede common sense, but it also depends on the school district. If the school board is dominated by fundamentalist Christians who want to stick their hands into the science curriculum, then problems begin to arise and children begin to not get the education they need.
A formal education has nothing to do with common sense. There are many people whom are book smart, but lack common sense. However, education builds skills, and skill builds common sense. So the cycle could be an unending circle. A formal education is very important and it takes common sense to do well.
If anything, formal education enhances someone's abilities to use their common sense to explore and discover. In addition they can use their common sense to come to new conclusions using the information they obtain through their formal education. In order to do this though one must not simply memorize facts in their education but be taught to develop critical thinking.