There is something that doesn't ring completely true about this. While I agree coding is not about coming up with some ninja recursive one line function that solves all the problems, reducing it to a simple matter of organization is not quite right either. Yes it is about organization, but there is a component of wizardry too. It takes a lot of intelligence, skill, experience and talent to be able to identify and mod…
If that is how it works, I did not really experienced it. In one place where they attempted this, senior ended completely out of touch with his architecture problems - because it was only juniors experiencing them and never him. In big corporations, architect does super uber high level and negotiations.
Big refactoring and architectural changes were done by seniors and require experience, of course. But that is only part of what senior does, a lot of if is using existing architecture. Also, juniors can grow into such senior only by taking on larger and larger tasks - you don't get there by filling small boxes without doing own decisions, mistakes and living with them.
The biggest problems, especially in larger projects, are organizational one. As in, algorithms part is what is often done by juniors, who often actually can do them well being just out of school and being trained in them lately. And also who have bigger uninterrupted chunks of time then seniors.