A lot of people might not like my answer, but here it goes. I have a 2,5 month old daughter, and my wife breastfeeds her. During the night, I don't wake up because she immediately gives her milk when she wakes up. There are a few things evolution gave us for support (correct me if these 'facts' are wrong): - When women breastfeed, they get some hormone that can put them into REM sleep way faster. - Men are not as sensitive for sounds during their sleep as women.
So evolution wise, this was probably mainly a mothers sacrifice. This lets the other, more physically strong parent (when that was still important) function at 100%.
In these modern times, work is divided and so both parents divide all family and money work, and so also share the sacrifice of sleep deprivation.