Rain Chains are very popular in Japanese Gardens and can add a nice esthetic touch, under most conditions.
Unfortunately, in areas where temperatures drop below freezing, their use can actually cause damage to a home from the weight of ice which can collect on the chains in winter. The nature of their design can allow ice to grow like a stalactite in a cave and they can actually hold much more weight from ice than can occur with a conventional gutter. Last winter's conditions would likely have produced monster icicles on rain chains.
I am very familiar with a special private garden in Ohio that uses them. I asked the owner about what he does with the rain chains in the winter. He said with a knowing smile, "The first winter the ice loading on the rain chains ripped out all my soffit and facia boards". He informed me before he repaired the damage, he had an expensive and elaborate support structure engineered, hidden and built behind the exterior soffit and facia.
Most of us probably can't afford to have someone perform the calculations necessary to properly size such a support system or to pay for its installation. I suggest if you want to have the look of rain chains, you should create a separate design to suspend the rain chains in such a way they are esthetic but they are not part of your functional downspout system. In addition, the rain chains should be taken down in the fall. In this particular case, your husband was right to be skeptical.