I was thinking I could use a tool just like the wire you described to remove a stump, after I spent 6 hours with a 5ton Bobcat trying to dig up a 3ft diameter pine stump to no avail today. For felling trees though, you need precise front cuts/back cuts to drop the tree at a desired angle, you can't just cut in one direction even if you have a cable attached.

Perhaps drilling in a wedge shape so it weakens the branch and it eventually breaks off naturally but it seems like more work than just a chain saw. The holes could also be used for steam treatment, enzymes [0] or something else to break it.

[0] https://en.wikipedia.org/wiki/Lignin-modifying_enzyme

I use a tool called the Alligator. Is is a tool you can use like scissors. It has 2 chains on the inside of the the business ends. You put around the branch. Close the end and press the button. Springs will then close the end even more and cut the wood. No open chains

I hear you on the safety angle, but chainsaws work really well. They're also very versatile.

We use a winch to guide the branches down, but would never apply the winch directly to the tree in case of whiplash when the branch finally breaks