What's an extra few minutes with your family worth to you? That's what it comes down to for a lot of people. I have limited and time and I am willing to outsource almost everything in my life that I can.
It isn't such a frictionless service though, you still need to find and hand off your keys and pass them off to whoever may be filling your tank and then do the same when receiving them. Which probably consumes all of 5 minutes on its own.
I doubt you can put a price on what's a reasonable price to pay for 1 minute of time with a member of your family. Is asking someone from your family to go with you to the gas station to fill out the tank while you chat about your day a reasonable way to spend time together?
This market mentality doesn't (shouldn't?) apply to social relationships because it leads to stupid decisions (like to give your CC number to a stranger). Next thing you're weighting how much your family time is really worth vs. making another buck.