This appears to have been the behavior of Piercing since it was first added in 1.14, but it still seems buggy and incorrect.

I would expect Piercing to behave as follows: With Piercing I, the arrow would pass through 1 entity, and would hit a second entity as normal. With Piercing II, the arrow would pass through 2 entities, and would hit the third entity as normal. And so on.

What actually happens: With Piercing I, the arrow passes through 2 entities. If it then hits the ground, it can be picked up. If it hits a third entity it vanishes, doing no damage.

In other words, the arrow will damage the expected number of entities, but its behavior after hitting the last entity is unexpected. It continues to exist, but will no longer damage entities, and vanishes instead.

See the attached video, where I demonstrate with every Piercing level. The particles and chat messages were added using a datapack to make the demo clearer.