Are car assembly plants really so heavily optimised for the human body?
Not really, but many of the machines in them are designed to be operated by humans.
Are human bodies so flexible in what they can manage?
Yes. Human bodies are incredibly versatile compared to any non-primate. Granted, there's things we can't do, but we've got a very good mix of abilities compared to other creatures. Our skin is a bit disappointingly fragile, but otherwise we're quite capable.
It all seems rather misconceived.
Agreed. It would make more sense to use robot arms with the tools redesigned to go on one instead of being operated by human hands. A lot of the tools are robotic already, for example the machines they use to tighten head bolts. A human only applies the tool to the head, it does the actual work. The human is there only for fine positioning! And it's not actually fine by modern standards, either.