[dmurray]

I don't see why. You don't show either passport to anyone when leaving the country. Instead they take your photo and compare it to the ones they have on file, which for a dual nationality citizen will include at least your passport photo.

I'm more surprised they don't want to physically stamp your passport. Even though they already have a record of you entering and exiting the country, they've always liked to have physical passport stamps. And losing those makes a material difference in the case where another country cares where you've been.