What it comes down to is there are trade offs. In the case of the engine, it's torque output and rotating mass versus engine speed ... read on.
First, it isn't power which is needed, but torque to keep an engine running. In the early days of engines, each had one cylinder and didn't run very fast. To keep it running, it had a very large flywheel attached to it. Once the engine was running, it continued running because there is a little physics statement which says something like, "mass in motion tends to stay in motion" and conversely, "mass at rest tends to stay at rest". The flywheel provides the mass which I'm talking about.
(NOTE: This is a single cylinder steam engine, but the same principle applies.)
(This single cylinder gas engine has two flywheel masses, one on each side.)
Today's engines are no different than those of old. They still require the mass to keep on running. Without some sort of flywheel, they will stop running. A manual transmission has a regular flywheel, which is its engine's mass. An automatic transmission has a torque converter, which is the mass for its engine. Without it, the engine will die because there isn't enough mass to keep it going between piston firings. The flywheel mass provides the torque needed to keep it going.
Even with this in mind, in order to keep an engine going at lower speeds requires the engine to produce more torque. Think of a large ocean going vessel with a diesel engine. The Wartsila-Sulzer RTA96-C is supposedly the largest diesel engine in the world. It runs, full out, at 127 rpm (that's typically 1/7th the speed of your average car engine). How does it stay running at this speed? Two reasons: mass and torque. The total mass of the engine is huge ... they don't advertise it directly what the rotating mass (crank shaft, flywheels, etc) of the engine is, but if you look at the video, you'll see what I'm talking about. The second part is the torque. They advertise that the KW output for their 14-cylinder engine @ 127rpm is 80,080 KW. If you run that through a few calculations, 80,080 KW converts to 107,389.03 horsepower, which at the given RPM is 4,441,001.46 ft lbs of torque. Your standard 4-cylinder car only puts out in the neighborhood of 150-180 ft lbs of max torque, and that's at a much higher RPM, say between 2500-6000. (NOTE: Some 4-cylinder engines can put out way in excess of this, say like around 300 ft lbs or even more. I'm just using the numbers as a general guideline.) It takes a minimal amount of torque to keep the engine running. I don't even think Jay Leno would contemplate sticking a Wartsila engine in a car (though I bet that doesn't stop him from thinking about the engine, lol).
The flywheel mass can only do so much. Once the crankshaft reaches a low rpm threshold, the engine will stop running. When an engine gets below this threshold and tries to continue to run, a large amount of stress is put upon the internal components of the engine. Think of the immovable object (pistons and rods) meeting the irresistible force (the air/fuel mixture blowing up). Once the engine slows down enough, its mass (as well as the mass of the car) reaches the point where it wants to rest (the other end of the mass-in-motion deal). Something has to give and that give usually comes at the cost of piston/rod. When you slow a vehicle down from speed while keeping the transmission in 5th gear, you will do what is called lugging the engine. You'll start feeling the engine jerking heavily until it quits running. This jerking feeling is what I was talking about when I said your engine will start experiencing extreme stress. If done long enough, the engine can experience enough stress to cause catastrophic failure. Even done for short period of time damage can occur.
So, bottom line is, an engine requires so much torque output to keep it running. As the engine slows down, that torque requirement goes up to keep it going. At some point, a small engine just does not have the needed mass, nor can it produce the torque which is required to keep it running.