Because cooking isn't everyone's idea of a good time.
That is kind of parenting. You put up with crap to teach your kids.
Also, cooking can be pretty fun. Again boils down to the kind of mentality you have and how you approach it.
Because then, when they are adults, they won't be discouraged because "it is too hard to get all the ingredients" or "it takes too long" because they'll have a better understanding of how to just roll with it. Maybe they won't be making fancy dishes ,but they also will understand how to do a twenty minute meal.
Case in point: You seem to think you have to be a foodie (screw that word and everything about it) to cook with your kids.
Going back to the sports analogy: No one is saying to force your kid to live outdoors. But taking the time to throw a ball around or take them on a hike or whatever conditions them to associate physical activity with fun which, in turn, encourages them to do it on their own.
As for family time: Why not both? My mother made it a point to have me hang out in the kitchen and help out and, as a result, I like cooking and know how to do things ranging from "What do I have left in the fridge?" to "Alright, let's make something fancy". Obviously having the kids use knives isn't smart until they are older, but just having them peel potatoes or hand you stuff is a good bonding experience. And, when they ARE older: you got yourself some cheap labor
And, to get back to the skillset thing: That really helps with saving time. I generally DON'T plan my meals (weekends when I am not out and dates are the only times I really use recipes). My food shopping is generally "What is on sale? Alright" and then I roll from there. And a lot of that goes down to being a kid and watching my mother figure out what was left in the fridge. Sometimes you make an awesome quiche or casserole. Sometimes you just throw some rice in a pot, saute some meat, and then throw a can of vegetables in near the end. And sometimes you are eating bologna and ramen.
Nobody sane is saying to go super all out or to never eat out/eat takeout/frozen food. But home cooked meals are generally healthier, a lot cheaper, and teach kids how to eat right and fend for themselves.