Do you all think that the Arduino kits would make a good match for this badge?

Yes, the Arduino controller would be a good choice.  As a counselor, though, I would encourage Scouts to use what they have.  If a Scout wanted to meet the requirements with his VEX or LEGO kit, I wouldn’t force him to use something else.  If you are thinking in terms of a workshop, camp, or a Scout who is starting from scratch the Arduino is great.