Given the generally terrible metal choices that goblin weapons are made out of, Copper armor gives sufficient basic protection from loss of limbs. Copper mail shirts and leggings are a vast improvement in protection over Leather armor. Copper armor will withstand attacks from the copper and silver weaponry that goblins sometimes bring. Iron or bronze or spears will cause problems, but even a little bit of armor can make a world of difference.
Once during a siege, an axe-goblin on a giant bat flew behind my walls, and as the bat randomly flew about, he brushed past my marksdwarf line, and in that momentary adjacency, with the swing of his axe, he cut a poor guy's leg clean off. If he'd been wearing even copper leggings, he probably would have just had the leg shattered with maybe some minor nerve damage.
Point is, copper ain't the best, but if Copper is your only friend, you certainly could do worse (I'm looking at YOU Galena). Any Weapon/Armor grade metal is a vast improvement over no metal.
Plus, if you have copper, Tin can be bought cheap from caravans, and bronze is a noble material. I have a fort where my wonderful mountainhomes (who sell giant cave spiders and crocodiles) are also able to furnish Cassiterite and Bismuthinite in abundance, so my plentiful copper can all be converted into glorious golden Bismuth Bronze.
It does make you wonder what the purpose of Dwarven colonies is though, since you always seem to be importing raw materials (lumber, ore, metal), and selling crafts. Do the mountainhomes have only the most basic of industries? I thought the purpose of colonies was to provide raw materials for the homeland. You won't get very far in DF though selling logs and metal bars. Maybe the purpose of the dwarven settlements is just to create new places for dwarves to live, and this effort is being heavily subsidized by the MountainHome. Why else would the traders be willing to give you bars of pure shining steel in exchange for a few tattered pigtail cloaks? Maybe the Mountainhomes are starting to invent paper, and are scrounging up all of the loose fiber they can get their hands on.
But I digress. It would be an interesting challenge to make a "Copper Only" fort, where your weapons and armor can only be made from copper, and see how well you fare against goblin attackers. Would have to be a "gates open" challenge though, since otherwise you can just make boatloads of copper bolts and shoot up anything that comes close.