I think the number of components could be zero if complete single cylinder engines are bolted together end to end.

A two cylinder or three cylinder is no problem. Four inline gets a bit long but might be doable.

If this were easily done, we would have already seen it, right? So why do we not see it?

Let's talk four stroke singles. Firing frequency is 1/2 per rev, with pistons going up and down at 1 per rev. Crank natural frequency must be at least 1.5x max rotational speed in revs/sec to put resonance out of range. Given the size needed on the power end for carrying pulley and belt loads, crank natural frequency is probably pretty high...

Now couple three together and stick a prop on one end. The crankshaft torsional stiffness just became one-third as stiff, and both prime frequencies just tripled. Only one flywheel is needed and it can be lower mass because you have the prop serving as flywheel. With crank resonant frequency dropping to somewhere around SQRT(1/3) = 58% of what it was while primary and secondary frequencies tripled, you very well could have all kinds of resonance issues walk right down into the operating range. Then the crankcases also have to keep their resonant frequencies safely above firing frequencies, and yet they have the same problems with stiffness dropping to a third and input freq tripling.

Then there is the whole issue of coupling one end of the existing crank to the other end of another crank. Coupling methods for the cranks and for the cases would each be pretty tough to solve.

In total, UGH.

This is why when engine builders talk about using more cylinders, they build shorter thicker cranks and shorter crankcases and shove the cylinders as close to each other as they can. For instance, the Porsche 917 engine, a 4.5l flat 12 is not just two 2.25l flat 6's. The Porsche 6's are boxers, each cylinder has its own crank throw with each opposed pair of pistons going out and in together. The 917 dispensed with that, with six throws to make the crank stiffer. These efforts make the crank natural frequency high enough to avoid resonance without it getting really beefy and heavy. What about yaw axis vibe from each pair of pistons both going the same direction that way? Well, the crankshaft front and back halves are mirror images of each other, so the cases have to stand the moments, but those forces are all internal to the crank case.

In multi-engine helos, they do not couple the engines together, they run an input to the gear box for each engine with a one-way clutch, among other things.

Now none of this is to say you could not do it, but there are a peck of challenges to making it all work.

Billski