The overall wisdom of this is a little questionable and crass of course, since there are also accidents that perhaps could have been recovered with more power.
I used to do a lot of gliding and the most powerful aircraft routinely flown was a Piper Pawnee (175 kW / 235 hp engine, in contrast to say c. 120 kW / 160 hp for a Cessna 172), used as a glider aerotow – and even then most of the time we had [electric] winch launches. The pawnee once memorably broke a cylinder head while on tow out and had a sufficient power reserve to both get the glider to a safe altitude and fly the rest of the circuit without issue. At the rest of the field, all of the GA aircraft were highly fuel optimised and mostly run by "normal people" worried about the cost per hour more than anything else. Even the aerobatic aircraft – CAP 10s – had less powerful engines than that Pawnee. I didn't see a super- or turbocharger, and the only people flying twins at nearby airfields were entirely doing it for the point of [commercial] pilot training.
Yeah I mean that's a good encapsulation of what I'm saying: the working aircraft have more power, but the cheap ones are mopeds in comparison. I guess maybe it is mostly the fuel economy though but it generally seems like moonies and other high-performance aircraft probably have much higher insurance/etc. It's cheap to insure your honda accord, you're not going to get yourself in trouble with 1.8L. The FAA is probably happier too.
Diesel could reduce the costs a lot, the DA42 (twin) burns 8 gal/hr, around the same as a C-172, and loiters at 3.2 GPH. Runs on Jet A too (diesel can run on kerosene). I generally think having more modern more advanced aircraft in general could help, the GA fleet is obsolescent and there's no money to replace anything, it's just 70s era engine designs and airframes because that's when the world stopped turning (apart from like, aviation schools and military).
Moving to a twin is a separate exam.
A big part of all those is the price of running the bigger plane/larger engine.
You could have a plane with constant-speed prop and fixed landing gear and it wouldn't be complex (unless it was a seaplane).
E.g., turbo prop (source https://www.quora.com/How-fast-is-the-tip-of-a-turboprop-bla...)
I double checked this math and got 474mph.
Meanwhile a Piper Arrow (4-seater piston, pretty comparable numbers to most Lycoming/Continental singles) takes off at 2700 rpm and has a 74” propeller, for a tip speed of 594mph. You can use a 3-blade propeller to reduce the diameter and cut noise somewhat (among other benefits).
Both of these are just the tip speed relative to the plane, I suppose you’d need to factor the airspeed too and use Pythagorean theorem but I’m no aerospace engineer.
As you noted, this is possible because the constant-speed prop on the turboprop allows it to take larger bites of air.
The Arrow needs that rpm to produce full takeoff power. However after takeoff it can be adjusted to a lower speed with minimal loss in power (e.g., 2500 rpm greatly reduces noise while losing 7-8% power). To reduce RPM like that in a fixed pitch you’d also need to reduce manifold pressure, causing more power loss.
If it had even a modest reduction drive, you could run the engine at a reasonable power setting while maintaining a more efficient tip speed but the prop and engine engineers had to meet in the middle resulting in a highly compromised solution.
Sure there have been improvements in modern engines, but these primarily target efficiency across power outputs whereas (as sibling noted) planes tend to have stable power requirements.
Not sure what your point is about constant speed or gearing because I already said that.
Is it? I've always thought that while GA engines are in many ways stuck in the 1940'ies, they are actually quite efficient. Wikipedia seems to back that up at https://en.wikipedia.org/wiki/Brake-specific_fuel_consumptio... , with a couple of Lycoming engines producing BSFC numbers in the same ballpark as a modern car engine or Rotax.
Edit: A dyno graph from an late 1990's Corvette C5 engine (5.7L) shows about 170HP @ 2700 RPM. That's at the wheels, so probably close-ish to 195HP at the crank: https://cimg5.ibsrv.net/gimg/www.corvetteforum.com-vbulletin...