You can pull hand- driven nails with a claw hammer or prybar if the inner edges are sharp enough, but it's clumsy and dents the wood all over.
A beekeeper's hive tool is perfect for doing that. They are cheap, and made from spring steel, so they pry really, really well. The hooked end can be pounded in and then exerts tremendous force.
I think I'm not making the task clear here. I'm talking about pulling the nail through the wood from the back side, head and all, like this:
So I can't see how a claw hammer or prybar (like that hive tool) would grip the smooth nail shaft. That's why I use pliers. The guy in the picture is using nippers, which I also never thought of but looks like it would work well.