Not at all. Most are grown without any trellis. It is just an option for those with small space to grow them. But if not then you have to have and allow the room for the vines to wander and usually mulch under the fruit to reduce rot from ground contact.

Dave

Concur. Korean melons don't slip so don't require slings as muskmelons do. An advantage when trellising.You still have to physically tie them to a trellis though. Climbing abilities are limited.

Several strategies to avoid rot. Another is to prop the individual melons up off the ground. Tuna fish cans do that well. Puncture to let them drain. I've put a bathroom tile under each melon. Turn them occasionally. Useful to control pests in the surrounding soil. I sprinkle the area around each melon with DE. I'm not aware of any melon vines that naturally climb. Not entirely clear if trellising is a net saving of work.

Thank You guys!