"Can't we just have a humanoid robot go and turn the screws for us?"

That would indeed be the best solution, if we can build such robots. Notoriously, computers are much better at "thinking" (or simulating thereof) than at folding laundry.

"it's now human lives on the line if things go wrong."

That is quite normal in many professions. Programmers are usually somewhat sheltered, so the very idea of risking your life on a job is shocking to them. But I grew up in a mining town and, well, some people will take that bargain for money. Some people even like the bit of a thrill.

I grew up in South Houston. I knew lots of families affected by workplace injuries at chemical plants and refineries growing up (for example, https://en.wikipedia.org/wiki/Texas_City_refinery_explosion ). I grew up going to Challenger Seven Memorial Park all the time. I had met a few of the people on the Columbia. Many of my friends had their parents go up in the shuttle afterwards, very clued into the risks involved. The idea of risking your life on a job is not shocking to me, it surrounded me from a young age.

I'm just pointing out the risk of failure and its impacts on the overall program is much higher when we're talking about humans experiencing a massive sudden depressurization event compared to a foil sheet failing to unfurl. If you think its expensive trying to get a foil sheet to reliably unfold once, imagine how expensive it'll be to design a door to properly seal and unseal hundreds of times with sharp, hard, and fine regolith constantly working its way into the seams and hinges and seals. If you think it'll be difficult getting public support after your telescope isn't perfectly functional, imagine the reluctance of funding you'll get when you accidentally kill seven people in a horrific way.

Luckily the robot doesn't need to be humanoid. The JWST deploying itself was one large, single-use robot.