Unless you intend for all archers to be forced into an 18/18 role in order to have full access to our classes capabilities, then you need to add a low tier piercing bow. Balance it as you see fit. But it should be available to low tier archers who are forced to go against all the heavy armor in game.
It should be slightly less effective against cloth, but way more effective against armor than the less than 1 hp damage it does now.
Edit: This is a revisit to this topic. Pasting my latest argument to the OP.
I made a post after the change from bow damage type to arrow damage type regarding the balancing of heirlooms by making a clear choice between damage and plenty of ammo. I think the difference between 0 pierce bodkins now and the ammo choice given with plain arrows (I've not been able to spam myself out of arrows even with a fast bow) has done what I asked.
However, I think I'm going to come back to my original request, which was to simply add one piercing bow at the low end. After playing around with archery and reading the feedbacks and complaints, I think that balancing by individual bow is just a smarter way to approach balance. Putting damage type back onto arrows has made it MORE difficult to get a good Archery balance, not easier.
Please, move damage type back to bows. Give Tatar and Long bow pierce. Move all other bow types back to cut, except for harassment type archer build (peasants), make the Short Bow damage type blunt so that peasant archers can at least get a decent interrupt.
Then go back to balancing by bow. It just made more sense.