I'd like to see this suitcase that these large-wheeled folders fold into. With room for a helmet. Likely large enough for the Titanic to fold into. Second piece of luggage, indeed! A suitcase that large would attract dizzying extra charges.
These fold into a 62" total dimension suitcase ; you know this I'm sure ? The same size that's necessary for a small wheeled suitcase, just that it will be squared instead of rectangular.
It's silly to check a helmet - you can always wear it through security and stuff it into overhead.