Tableau will not stretch and distort the view just to fill the entire paper, it will enlarge one side until that side fills up all available space and scale the other side in proportion, i.e. you cannot get a square view to fill all of a rectangular page. If the dashboard has a scrollbar with more stuff at the bottom, this will not print - only currently visible part of the view will.
Sheets don't have this problem - Tableau will spread them over multiple pages, if required.
That is really surprising. Seems like pretty basic feature. Thanks for the advice.