The sag is what allows you to lie flat in comfort. If you strung it like a trampoline it would force you to conform to the hammock, just like the ground forces you to conform to it, and it would be no fun at all. An air mattress or water bed will conform to your body and be comfortable, in similar fashion.

Hammocks look different from the inside.



That's a hammock without the pad - here is the hammock with the underquilt, minus occupant. It does look like a tube. Just not when you are inside it and spreading it out around you.