Why the lack of faster piston-powered planes? There aren't very many fast piston airplanes in production. By "fast" I mean, if you look back in the early to mid 20th century, before turbines won out, there were lots of piston airplanes in production that pushed the practical velocity limit of propeller-driven aircraft, cruising 360+ knots in military planes, sometimes as fast as 330 knots in commercial airliners. And this was with a terrible understanding of aerodynamics and piston engines compared to today.

Today, for both singles and twins, the fastest speeds around aren't much higher than 200 knots. ~240 knots in the case of the very fastest couple available airplanes like the Cessna 400 and fastest Mooney.

There are indications that with modern materials and engineering, much faster speeds can be achieved using piston engines already available. The Cobalt CO50 Valkyrie design claims to push a spacious 4 person cabin up to 260 knots with a single 350hp engine. The recently-certified Diamond DA-62 can move a spacious 7 passenger cabin at ~200 knots using only a pair of 180hp engines.

Why aren't there more faster piston airplanes available? Would the market not be interested in piston powered planes that could do 300 knots? Shouldn't you be able to make almost those speeds for a very small plane powered by a single commonplace 350hp engine? Shouldn't you be able to make those speeds in a more spacious plane with a pair of commonplace 350hp engines?

My understanding of the marketplace is that the #1 reason people choose piston is cost. And isn't the cost of operating piston engines, even two piston engines versus a single turboprop, much much lower? How much does a 350hp turbocharged piston engine cost brand new, 50k-60k dollars? So even buying a pair of them is 100k-120k dollars. And then how much does a single comparable turbine engine cost? ~800k dollars with proportionately higher rebuild costs per flight hour? Plus 20%+ higher SFC than a piston?

Basically, I see the Piper M600 listed at 2.8M USD, or the TBM930 listed at 3.9M USD, and I don't understand why it would be hard to achieve nearly the same performance for a fraction of the price using a pair of cheap piston engines. For example the Piper M350 has the same 6 passenger cabin as the M600 and also includes pressurization, and with a single 350hp engine makes over 210 knots on a very old airframe with a list price of under 1.2M USD. If you basically built the same airplane but reoptimized for twin engines and using modern materials and aerodynamics, shouldn't you be able to achieve near 300 knots by adding another piston engine? And shouldn't you be able to sell the resulting airplane for well under 2M USD and with a significantly advantaged SFC and therefore range and payload than the M600?
The power requirement of an airplane grows with the cube of speed. When you fly fast with an airplane which needs to comply with a set minimum speed imposed by regulations, your drag coefficient is nearly constant, so flying faster does two things to a propeller aircraft:


Drag goes up with dynamic pressure, which is proportional to speed squared
Thrust goes down with the inverse of speed.


Power is thrust times speed, so if the the 350 hp get you to 210 knots, doubling the installed power can only bring you to 264 knots. A turbine can still make limited use of the increased dynamic pressure by ram recovery, so here the thrust decrease over speed is not quite as bad as for piston engines.

Expressed in an equation, the power $P$ demand for a given speed $v$ is:
$$P = \frac{D\cdot v}{\eta_{Prop}} = \frac{\rho\cdot v^2\cdot S_{ref}\cdot c_D\cdot v}{2\cdot \eta_{Prop}} \rightarrow v = \sqrt[\Large{3}{}]{\frac{2\cdot P\cdot\eta_{Prop}}{\rho\cdot S_{ref}\cdot c_D}}$$

If you want to fly fast with better efficiency, you need to increase the minimum speed - note that the landing speed of many fast piston aircraft was around 100 mph. Now you need a long runway, and for operation in bad weather or at night infrastructure for instrumented approaches, and you will end up at airports where turbine fuel is easy to get and cheap, but piston fuel will be hard to find and expensive.

As with all expensive machinery, you need to use it often to justify the expense. Now your fuel cost will factor in, and will make a piston engine rather unattractive.

Fast piston aircraft were only built while turbines were not yet available. As soon as turbines emerged, all fast piston designs were obsolete. And aerodynamics in the early 1940s were already very advanced; engineers back then built airplanes which would be impossible to design with the engineers of today. Back then, they got fully manually controlled airplanes into the air when today everyone would refuse to do it without hydraulic boosters at only half the flight speed. They could design cooling ducts which actually increased thrust, an art which is (almost) lost today.