I'll be damned if I chip my nail polish on manual labor these days. Not because I'm "above it", but because I hate it with a passion. If I can pay somebody to do it for me, awesome. If they actually enjoy their work (and many contractors do), it's a win-win, as far as I can tell.
As for family time, and I say this as one without kids, if the kids are old enough I can't think of a more valuable way to spend time than teaching your kids to build something.
Well, this firstly requires the kid is interested, secondly that the task at hand is approachable by a kid (e.g. painting instead of transmission work), and thirdly that you have the time to tutor them while you make the repairs.
Not to say it should not be done, oh no! But it is not always an option.
I feel that the lack of free time is attributable to a large number of "ills" for society, from the lack of participation in civic duties, to lower voting rates, etc, etc.
Just remember to let your car cool off before trying to replace it. Made that mistake a couple times!
It doesn't surprise me, either. My father was very much that type of father. I luckily picked up a lot of the skills on my own volition, but already I choose to pay someone else to replace my radiator when I could do it myself, even though I am yet unencumbered by family duties.