Silk

The first real reason to make any is a bed, and a bed is what lets you set a spawn point that is not the middle of the world. That makes the first cobweb run into the caves a soft progression checkpoint, and it comes earlier than most people expect.

Raw cobweb sells for nothing at all. Woven, it has a price, so a loom pays for itself the first time you strip a spider nest. It is a slow trickle rather than an income.

Once you have bones as well, stop selling it. Turning the same cobwebs into Necro Helmets and selling those returns several times as much for identical gathering effort.

Past the bed it is a furnishing and vanity material. Sofas, banners, swimwear, the Ancient set and a long list of clothing all want it. None of that is urgent, which is why a stack of cobweb never really goes stale.