You don't need high-speed exhaust, and in fact there are good reasons (mostly noise abatement, but also efficiency improvements) to reduce exhaust speeds, which is precisely what turbofans and exhaust bypass systems on modern day commercial jets do (military planes don't, but they operate without noise controls and in a high-performance envelope in which efficiency is a secondary concern).
What jets offer over propeller-driven aircraft isn't efficiency, but speed, and power-to-weight ratios. Propeller aircraft are limited by the tip speed of propellers (they have to be below the speed of sound), but are often much more efficient especially at lower flight speeds.
In terms of efficiency, jet aviation has largely just managed to catch up to where propeller-driven aircraft were in the 1950s, when general-aviation jet aircraft first came into general use (barring a few failed Comets).
I agree with you that electric aircraft are not particularly feasible, small drones excepted.
What jets offer over propeller-driven aircraft isn't efficiency, but speed, and power-to-weight ratios. Propeller aircraft are limited by the tip speed of propellers (they have to be below the speed of sound), but are often much more efficient especially at lower flight speeds.
In terms of efficiency, jet aviation has largely just managed to catch up to where propeller-driven aircraft were in the 1950s, when general-aviation jet aircraft first came into general use (barring a few failed Comets).
I agree with you that electric aircraft are not particularly feasible, small drones excepted.