I get what you're saying and maybe zen or meditation isn't necessarily the right words to describe it. More like a stress reliever. Like a punching bag with a productive outcome that adds to its satisfaction. For me, the wood does not need to be cut, yet I cut it. Maybe someday I'll need firewood and I'll be ready.
I might be a little more country than this community, but exercise to me is grabbing wood from the local yard waste site to split by hand. Some good clean fun to clear the mind and keep the body strong, and just the right amount of danger to keep it interesting. Not to mention the lifetime supply of campfire wood.
I maybe just might also like to grab wood that requires a chainsaw because chainsaws are neat(fricken awesome). It actually takes all my restraint to not start a rampage through the local woods. It's addicting, the chainsaws not deforestation. I'm a tree hugger by nature and deeply conflicted by alot of human's creations.