The US has plenty of manufacturing operations much more complicated than building CPUs

It's my understanding that this is not the case. That CPU (and similar) manufacturing is considered one of the most complex processes humanity has ever developed. What are these plenty of manufacturing operations that are more complicated?

It really depends on which part of the process you focus on. CPU manufacturing is highly automated and not particularly logistically complex. You're correct that the machines used are just about the most sophisticated things ever built by human hands, but once they're installed and configured the process is fairly straightforward.

Compare this to, say, building a car. Much less automation, much simpler end product.