The thing where is 99% of the complexity and you can't redesign in a month is the infrastructure, how data is stored, how the various components communicate together, how everything scales globally, and all the related components. Things like Twitter are not complex for the application (that is trivial to implement) but for what it takes to run that trivial applications with that kind of numbers.
Looking only at the code is stupid, since code is fairly trivial to rewrite, while doing infrastructure changes is something difficult, costly and in some cases even impossible.