The point of a rebuild is not to preserve the old mess with more modern tooling. If anything, that is the most efficient way to waste time while pretending to improve something.
What the new site needs is a stronger container for the work itself. That means clearer structure, better defaults, and fewer hidden dependencies waiting to make publishing feel annoying six months from now.
A good container does not make the work less strange. It just stops the scaffolding from competing with it.