I suppose eventually it could be a rack robot instead, why not.
Self driving cars already work well in niche (millions of people have used them successfully). There is debate over how well (the only people with access to real world data who are talking also have a clear bias so who knows), but they at least work today.
There are a lot of order systems that automatically order parts for you. Just in time and tracking what you ship makes it easy for a program to figure out what you need. If you order something from my company the system automatically orders all the parts needed to arrive the day we assembly in our factory (which is very automated and getting more automated all the time).
I'm sure places like Dell have a lot of automation in their build a server, though I don't have insight into how they do this. Likewise every medium sized company has images for everything so all the software can be automatically installed.
None of the above is perfectly human free yet. However it has been moving that way for years and will continue to. LLMs have a place in moving that long.
What you describe sound extremely expensive, even from a future perspective. It doesn't make any sense. And for larger businesses who can afford things, we already have quasi automated date-centers from AWS and others.