Is it, or how might it be illegal to build a small shack in a non-private/non-commercially owned wooded area where no one ever goes?

It might be illegal ONLY if you don't have whatever permission is needed from the owner and whoever regulates construction of "small shacks", if anyone. Not sure what "non-private/non-commercially owned" means. A commercial owner IS a private owner, since they're not a GOVERNMENT owner.  So, maybe you meant "government owned"?  Yes, there are thousands of shacks built upon government land legally. So, there's that.

Non-private? You mean it's government property? If it's not your (private) property, you have no right to build there.

The land has to be owned by someone.  It's called trespassing.

It would be illegal because you do not own the land.  Therefore, trespassing.

In MY Sate it's trespass.  Are you saying the Government owns the land?  Again, in MY State it is trespass, and if you can be identified you can be charged to remove the "shack."

Laws depend on where in the world you live............. unless the land belongs to you generally it is illegal to build anything as you don't own the land however even if you did own the land, you may need to seek building permission

If it's State or Federal land, it's illegal.

If it's a nature preserve, wetland, or special habitat it's illegal.

If it's in an archaeological site, it's illegal.

The purpose of the shack may very well be illegal regardless of where it is.

You can probably get away with it for awhile till the owner finds out. Here in mi there are cabins in remote areas on federal or state forest land. But it is nearly wilderness conditions used only by hunters or hikers.