In the context of this post it's not about preserving or sharing the thoughts. Writing, in this case, is a "thinking tool". Forcing yourself to materialise the thoughts as actual, written, text helps form clear ideas.
To me, if the problem is too complex, or more likely, if I expect to be distracted by family and chores, "building in my head" is not the best option as it all falls apart and need to build it up from scratch (though admittedly faster than last time).