Mxsmanic wrote:

However, turbofans don't work well at transonic and supersonic speeds,
although I understand that these problems have been fixed in recent
years. Likewise, they don't have significant advantages for low speed
flight like that of a small GA plane.

Turbofans work very well at transonic & SS speeds. The engines in the
F-15, F-16, F-18, F-22, F-35 (you get the idea) are turbofans (w/
afterburners). The F-22 engines are so efficient they allow supersonic
flight without the burners lit (supercruise) The difference is they are
low-bypass turbofans compared to the big high-bypass engines on
transport category aircraft - (Boeing, Airbus)

Turbines burn lotsa fuel at low altitudes and are most efficient at
high alts, which normally requires pressurization. Your typical GA
plane doesn't fly at high enough altitudes to get the most benefit from
turbine power.