I think quantity matters a whole hell of a lot more than people give credit to.
Quality time was probably a phrase developed to make working parents parents feel better about their time away from their kids I think, to relieve guilt. I am not making any personal judgement about working parents or time away, I am just commenting on what I hear from so many moms especially, how guilty they feel. It also was to encourage men to be more present for their children I think. To show up for football games and ballet receitals, etc.
Personally, I think young kids care more that they see their mommy and daddy daily, in the normal course of the day, then very special events once a week or once a month. Even as children become teen, they may not want to be bothered by their parents, but they want their parents to be there available.
I do think it is very special to have specific memories with a parent that was full of fun and happiness. A trip, time at the beach, watching a drive in movie, going to the pumpkin patch, but those things do not replace daily presence in the home or daily attention in my opinion.