A lot of these skills generalize way beyond the immediate problem. I don't have a "fix the faucet" skill, I don't even think in these terms - more in terms of "operate wrench", "operate set of screwdrivers", "understand how water faucet works", "understand how plumbing works" (at high level), and these skills let me diagnose and fix many problems myself, most of them not even related to water faucet. Etc.

Other considerations:

- Sometimes you need a solution NOW. Household infra tends to break down on Saturdays and Sundays a lot for some reason.

- Sometimes it's not even about efficiency. Like, we got ourselves an allotment garden recently. Per your $100/hr vs. $30/hr math, I could and should just hire a bunch of contractors to clean it up and set it up for us. But for me, this defeats the point of getting that garden in the first place.

- Some work is too small for a contractor with necessary skills to come, unless you let them bill you for 10x the work. I had to learn how to patch holes in ceiling myself, because the price for getting the 4m x 5cm hole fixed was the same as for renovating the whole ceiling.

EDIT:

Also what 'lotsofpulp said - sometimes you want the outcome to have a very particular shape or quality level, and to guarantee it, you'd need to micromanage the contractor so badly, that in many cases it's easier to do it yourself.