The important feature is not so much the flat sheet, but vertical threads that rise like a scaffold to overhanging parts of the plant. A flying insect comes zipping along and crashes into one of the threads. The momentarily confused victim falls to the sheet below and is quickly caught by the alert spider. Sticky scaffold webs lacking sheets are common among a particular group of small spiders, but when I studied one of their kind native to Pacific island rain forests, I found it relied more upon stealth and leaf vibration than upon web-building. Other kinds of spiders use silk in ways that almost defy belief.
Dinopid spiders make square nets held widespread between their legs.
When an insect flies by, the net is cast to enmesh the victim and is then gathered back in precisely the same way I've seen Polynesian fishermen use nets to snare reef fishes. Another spider makes a replica of a South American bolas with a sticky blob at the end of a long thread. The weighted strand is twirled and thrown directly at a flying insect. If such methods aren't sufficiently awesome, there are spiders that have dispensed with silk entirely and instead spit a zigzag band of glue so quickly a victim is immobilized in the blink of an eye. When an insect hits outer portions of the diaphanous disk, vibrations travel down the non-sticky radial threads to the center and the spider instantly knows in which direction to head.