Broken mess?🤨I don't know where you are seeing this.
NYC buildings look fine in F4, streets.gl, osmbuildings, mapbox. Some how more details, some have less. Some could be improved. But it's hardly "a real broken mess".

I think you are misunderstanding the statement you quoted.
Yes, if there's a way with building:part=yes exists within the perimeter of a building outline, building outline is not rendered. That's not broken. That's by design.
It is so that the whole building can be correctly and accurately represented by all the necessary building:part=yes ways.