There's one rather serious flaw in your comparison here, at least when comparing GA flying to driving, and that it's very rarely that either your departure point or your destination is an airport, and practically never that both are.
I'm going to give you an example. I live in Roswell, GA, and my mother lived in Brooksville, FL. Every year around the holidays we'd go to visit her. According to Google Maps, it's 445 sm by road, and 6.5 hours. My experience tells me that this is correct. We'd usually add a lunch stop in the middle of that, but in terms of travel time, 6.5 hours is a good figure to use. My car is a hybrid, and it usually got 37 mpg southbound and 36 northbound, 12 gallons southbound and maybe 12.5 northbound.
I'm going to use the OP's 172N as an example. My father owned one in the 80's, and I'm very familiar with it. The closest airport to my house is Cobb County/McCollum Field (KRYY), and the closest airport to my mother's house is Brooksville/Tampa Bay Regional (KBKV). I couldn't find a direct distance, so I used KATL - KTPA, which is 353 nm. I used the 172N POH figures for taxi and takeoff, and the figures for flying at 6000 feet at 2500 RPM, which is 67% power, say we cruised at 5500 feet one way and 6500 the other, and I assumed a 10 knot tailwind southeast bound and a 10 knot headwind on the way back.
There are four of us, and we weigh about 610 pounds, and would have about 100 pounds of baggage, which leaves 190 pounds for fuel given a 900 pound useful load, which is 31 gallons. I have a rule that if l don't have an hours worth of fuel at cruise setting, when I land, I was reckless, and I don't like being reckless.
The steps to get to my mom's using general aviation would be this:
Drive from my house to KRYY: .5 hrs, 16 sm, .4 gallons
Get plane out of hangar, preflight: .3 hrs
Taxi, takeoff: .3 hrs, 1.1 gallons
Climb to altitude, .2 hrs, 1.9 gallons
Enroute, 2.8 hrs @ 125 knots, 21 gallons, 353 nm
Approach, land, taxi, .2 hrs, 1 gallon
Secure airplane with FBO, .2 hrs
There are no rental cars based at this airport, but there is an Enterprise office 9 miles away. There should be an unknown amount of waiting time added here for a ride to their office, but since that's unknown, I'm going to leave it out.
Ride to Enterprise .3 hrs, 9 sm, .4 gallons
Rental car paperwork, .2 hrs
Drive to Mom's, .2 hrs, .2 gallons
Total that up, you get 5.2 hours, 30.4 gallons, That's shaving off 20 percent of the time of the drive, but uses 140% more fuel, plus is quite expensive. A 172 is cramped and loud, and lacks air conditioning. A sedan is quiet, spacious, and comfortable, and if someone needs a bio break, that's typically less than 15 minutes away when you're driving.
On the southeasterly leg, we enjoyed a slight tailwind and used 24 gallons. That left us with a 7 gallon reserve, which is close to an hour at 65% power. On the way back, everything is the same but the enroute portion, which goes from 2.8 hours to 3.4 hours, and from 21 gallons to 26 gallons, and our fuel reserve is essentially gone. We now have to make a fuel stop, which will consume at least .7 hours and five gallons. This means that the trip northbound is now 6.5 hours, the same as the car, while using triple the fuel.
The other issue is that the flight requires a lot of steps, and if something unexpected happens, the time advantage is likely gone. With car travel, the most common unknown is traffic, but for the most part, you can plan to miss most of it. And of course, the dispatch reliability of car travel is vastly better than that of light GA. If I'd planned to make this trip today, all I had to do this morning to tell I wouldn't be flying is to look out the window, we had storms until afternoon.
Most pilots fly because they enjoy it, not for any practical reason. There are certainly people who can get some utility out of flying light GA, but there aren't all that many. If you like to fly, by all means do so, but I think you're doing yourself a disservice, especially if you have to come up with logic like you have here where an increase of speed is worth the square of the effort needed to create it, in order to justify your flying. At the end of August, my younger daughter is returning to school, and she's never driven long distances by herself, so I will be driving up with her, and she will drop me at KCLE and I will fly back on Delta. The flight back is about an hour and 45 minutes, and is $120. If Delta offered service that would get me back in half the time for four times the price, I would say no, it's not worth $360 to save 50 minutes. I'm afraid that your rationalization here does not stand up to scrutiny.
Should I post this as a reply to your blog?