Yep, ask their reasoning. I have thought about this too as a parent. I think I too would have an easier time with the exchange than a summer at a friend's. My reasoning? Responsibility and structure. As a parent I would be concerned about things being somewhat laxer at a friend's. Also, there exists a sense of purpose around an exchange which is not apparent with a long term visit with a friend. I would have a great deal of high expectations of your friend's parents too. Just my thoughts.

On the other hand, kudos to you for the suggestion you work.

What might help you in your favour?

A clear list of rules and expectations you are prepared to follow. An explanation of the complete purpose and outline of activities, etc (what are you going to do to ensure it is an enriching experience?) you intend to undertake. Perhaps even an example of your intended routine. All of these things I think would go far in demonstrating to your parents the positives for such an endeavour.