Why are two-stroke engines nearly unheard of in aviation?
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.