Why are two-stroke engines nearly unheard of in aviation? Almost all aircraft piston engines are four-stroke engines, with one power stroke per piston every other crankshaft revolution and a great deal of intricate moving parts which are only too happy to break.  Two-stroke engines, in contrast, have a number of features that would seem to make them excellent choices for aviation use:


They have one power stroke per piston per crankshaft revolution, twice as many as a four-stroke engine, and also have far fewer moving parts, making them smaller and lighter than four-stroke engines of the same piston size and count; these two factors add up to give them a phenomenally high power-to-weight ratio, much better than that of a comparable four-stroke engine.
The same mechanical simplicity that contributes to their high power-to-weight ratio also makes them cheaper to build and sell, and (all else being equal) more reliable than four-strokes.
Most two-stroke engines are lubricated by mixing lubricant into the fuel rather than using a traditional oil sump; this allows them to operate happily in any orientation, including upside down.


The sole disadvantage of two-strokes is their greater fuel consumption and emissions, but:


Good design can reduce this problem to insignificant proportions;
Higher fuel costs could easily be offset by the reduced maintenance costs of a more reliable engine1 and the ability (due to the engine's greater power) to use fewer engines per aircraft, and;
When it comes to piston-engined-aircraft emissions, there are far worse concerns.


Yet, despite these advantages, to the best of my knowledge, only one two-stroke aircraft engine has ever entered mass-production (the highly-unusual Junkers Jumo 204/205/207 series), with a second (the Rolls-Royce Crécy) being cancelled during static-fire testing.

Why are two-strokes essentially nonexistent as aircraft engines?



1: Especially given that maintenance costs are often (though not always) a greater expense than fuel costs to begin with (scroll to page 20); the linked document is discussing jetliners, but the preponderance of maintenance costs would be much more pronounced for piston-engined aircraft, as piston engines are considerably more efficient and considerably less reliable than turbine engines (the latter due mainly to their massive mechanical complexity).
Several issues:

As you mentioned, high specific fuel consumption.  About to that of turboprops, but without the reliability. If you're going to live with that SFC, you might as well as go with turbines.

Poor reliability.  They are very sensitive to tuning and timing.  A 4 stroke piston aircraft engine will run with all kinds of things wrong with it.  Cam lobes worn down to nearly nubs.  Loose valve guides.  Horrible compression.  They can have compression readings that will cause most mechanics to ground them, but they will still make rated horsepower (Continental did testing to find this).  They are very "under-tuned", like a tractor or industrial engine.  You want this in aviation.  About the only thing that will make a 4 stroke aircraft engine blow up in your face is something like a thrown rod from a spun bearing or a cylinder that cracks open, and that requires bad maintenance or criminal neglect in the vast majority of cases.  2 strokes, in the ultralight world where they are widely used, have a reputation for letting go at any time (the only 2 stroke aircraft engine that even comes close to 4 stroke reliability is the Rotax 582 - but only close, and they're only reliable for a few hundred hours).

2 strokes require pressed together cranks with ball bearings because they have to depend on lubrication from oil mixed in with the fuel charge. So you can't have a forged one-piece crank (radials get away with ball main bearings but there is only one or two crank throws, and they still have dedicated oil lubrication).  With the only oil coming from what's diluted in the fuel in a 2 stroke, piston ring lubrication is marginal and ring life is poor.

Which gets us to longevity.  Although it has an official TBO of 2000 hours, if you take decent care of it, a Lycoming O-320 will run 3-4000 hours.  The plain bearings in a 4 stroke only see wear on startup; there is zero wear once they are pressurized because there is no metal to metal contact, and if you never shut it down and changed the oil on the go, the bearings would theoretically last forever.  Ball bearings lubricated with diluted oil have a finite life, and that and the barely lubricated rings limit longevity. You would never dream of a 2 stroke lasting that long in any galaxy in this universe.

2 strokes are popular in the ultralight world almost totally because they are cheap and have a superior power to weight ratio. You almost get a turbine's power to weight, and minimal cost, and that's worth living with the crappy reliability.  Ultralights get away with it because they crash going 30 mph not 70.

Problem is, a lot of the issues are baked into the configuration and can't be designed out.  Combine with with a business that is conservative by necessity, because your life depends on the conservatism, and it's no surprise.