The value is in getting them to write down what happens step by step as their program executes.

Writing things by hand can just help facilitate that because it removes the ability to run the program and get the final result.

People can lean on their tools to 'guess and check' their work. Write a loop, run the program, and get an out of bounds error. They'll have learned oh this error means I need to subtract one from my loop bounds. And sometimes that works, though many times, it means there's an edge case they didn't properly handle.

When you only have pencil and paper and you need to explain to me what your code does you have to write down a representation of what's in memory and then how it changes step by step as the code runs.

I would be way too impatient to write code like this. It is hard for me to imagine how anyone could do this. I guess I do not really get this, it almost feels to me like people want to be hipsterish a bit. But of course I am likely wrong.

I have no citation, but I’ve been told that writing something out by hand stimulates different parts of the brain, as does explaining that thing out loud.