Niels responds to an old question.
Pushrod valvetrains in big engines (~500 cubic inch class) limit out at about 5000 RPM. Going faster than that usually requires an overhead cam and might yield ~6000 RPM, but past that the reciprocating mass tends to make the engine explode unexpectedly, so to go still faster (and make more power) you reduce the piston size and the crankshaft stroke and add more pistons to maintain displacement.
So instead of a 6-cylinder engine you now have a 10-cylinder engine, and you might make that monster spin faster with dual overhead cams instead of singles. But now you run out of lubrication capacity in the main bearings, so you re-engineer the engine for roller bearing mains.
Now you have to re-engineer the heads for higher heat-rejecting capacity so you do not overheat the exhaust valve seats, which means water-cooling and perhaps also forced-oil cooling.
Now the engine requires supercharging to overcome its pumping losses, so you bolt on a blower to make it spin faster and make more power... but all of this produces a big problem, as follows:
Every crank revolution wears the piston rings, bores, valve train components and crank bearings a tiny little bit. The useful lifetime of the engine is set by how many crank turns you can accumulate before the wear limits are hit. And this means that if you gear the engine down to spin the prop half as fast, you'll accumulate crank turns twice as fast per hour of flight time and you cut the TBO in half- and now you have to overhaul the gearbox and the supercharger as well as the internal engine components in 1000 hours instead of 2000 hours.
Drag-racing engines can push to 7500 RPM or sometimes 10,000 RPM and produce a thousand horsepower or more out of 500 cubic inches, with a TBO of several minutes (no kidding!)- and crowd-pleasing (i.e., truly spectacular) failure modes if any little thing happens to go wrong. So...
High reliability and long life dictate minimizing RPM's and engine complexity, so in internal combustion aircraft engines you stick with big pistons, direct drive, natural aspiration and you live with half a horsepower per cubic inch of displacement at sea level.