Is $4,700 to repair an exterior drain pipe with a tree root clog a fair price?

I just bought a home with an exterior basement stairwell. Shortly after buying it, I realized that the drain at the bottom of the stairwell is clogged with a tree root, and it doesn’t work at all. It looks like a tree root broke through the terracotta joint from the pipe and ran further down the pipe, displacing the portion of the pipe that connected to the terracotta. I'm worried this could grow into my home’s plumbing. My wife and I considered removing the door, rebuilding the foundation wall, and removing the stairwell, but that wouldn't address the root issue. I'm at a loss as to how to handle this problem and am looking for suggestions on how to cap off this exterior drain before spending up to $9,000 on an exterior basement stairwell that is nothing but an eyesore and a liability.