This is pretty fun to use with mods that allow for cosmetic armor slots. It would be cool if the wool clothes could allow for banner patterns to be applied to the chest or something similar.

OR, if you could apply images to the wool chest like an item frame, but limited to 2D items so they don't look oddly textured. I'd wear a black shirt with a diamond on it!

OR, if the sewing table could be used to created padding that could be equipped in Curios slots for extra armor, and maybe even accept enchants. Heck, wool armor is basically padded armor. Then you could upgrade wool padding with leather to improve the armor rating, add toughness, and so on. Chains and chainmail armor could be used as a third tier (sewing pads and leather into the chain mesh). Fourth tier could incorporate sewing in iron plates made from ingots.

Ingots could be used to make grommets, zippers, and other metal sewing parts.

Last thought: rotten flesh pants. Making clothes that use mob parts could create an intuitive way to swap skins to look like mobs. These mob clothes could maybe cause matching hostile mobs to because passive as an incentive to make them. Once again, great synergy with cosmetic armor and Curios slots!

I would like to bump the Curios option as well (especially as it'd be an excellent example); I did try to add the wool hat as a head curio (via a datapack) with no success.

Curios doesn't normally have a head slot out of the box, are you using some mod that adds a head slot to curios?

Artifacts [https://www.curseforge.com/minecraft/mc-mods/artifacts] does, then. It probably adds the feet and hands slots, as well, and perhaps some others.
To clarify, I was able to successfully register the wool hat as a head curio, and equip it (and it probably would have added any stats,). It was just invisible.

I see. I understand the request then, but I don't think I should be the one to add curio rendering to my items. It should be on the mod that adds cosmetic armor slots to do the rendering of any armor piece they are handling.
My wool items are exactly as any other armor item, so on a cosmetic slot, they should work exactly as any other armor item. If they don't I would blame that on the mod adding the curio slots.

I could see that; and that would make it dependent on Artifacts too, which is also getting way too far into the weeds.
I think a better approach would be a datapack adding sewing kit recipes to a Curios mod; I'll see if there's one I like enough to spend the time.