There are many businesses that have gone through generations of the same family. In some families, this is an expected tradition that children, grandchildren and great-grandchildren will carry on. I imagine it would be a very special feeling to be living where you ancestors lived and working where they worked. You would probably feel very close to your family. As long as they enjoy the work and are happy where they are living, I don't see anything wrong with working where your parents also worked.
I would work in the same profession as my parents as long as it pays well. If my parents were in business I would gladly follow that path, but if the returns are not going change my life i wont engage in it. Just look at the standard of living of your parents and decide if you want to end like them.
The Tabasco company has had many generations of the same families work there. Indeed, some children end up working in the same profession as their parents. However, most want professions that are different from their parents. The Tabasco company is kind of the exception instead of the norm. There are very few companies around anymore that have had so many generations of the same families work for them. In short, no, most would not want to work in the same profession as their parents.
While many people at Avery Island, work at the same company as the forefathers did more than 100 years ago, this is the exception. I would like a different path than my parents. My parents worked hard, but were in blue collar professions and stressed the importance of education. Therefore, I have chosen a different road.