Happy families are all alike. every unhappy family is unhappy in its own way.--Tolstoy.
If the parent isn't causing conflict they may well be detracting from it by giving the main characters too much support so they don't suffer and struggle and drive the plot forward.
There's always the silly parent, a la Pride & Prejudice, too. But Darcy is an orphan. With parents he'd seem so much less alpha. Plus he wouldn't have inherited!