When I was poking around to find example discussions of swapping/popping for my previous thread, I came across several sub-discussions about struggling to swap pie charts.
The reason pie charts don't swap well is because most examples of building pie charts don't have any dimension pills in ROWS or COLUMNS.
I have found that a sheet completely "disappears" when filters cause no data to be found only if there is at least one dimension pill in ROWS or COLUMNS. If nothing is there, the sheet goes blank, but the sheet still holds onto its boundaries. It's the difference between an empty sheet, and no sheet at all.
So this principle holds whether your viz is a pie or bars or text. It's just that the pie chart method lends itself to making a viz with nothing in rows and columns.