1. Turbine Efficiency
In 1923, Edgar Buckingham published a report regarding the efficiency of gas-turbine engines. According to his calculations, a gas-turbine would become more efficient with speed, but would be 1/4 that of the piston/propeller combination and unsuitable for operations.
If you have looked at Buckingham's report then read no further. If not, I have noted a couple of things.
He wasn't referring to a gas turbine. His arrangement, what he called an obvious alternative to an airscrew, replaced the propeller with a piston compressor, combustion chamber and propelling nozzle.
From a propulsive efficiency point of view only, both speeds which determine it were very different from subsequent gas turbine applications.
His aircraft speed was 250 mph. Whittle's enthusiasm for jet propulsion was for speeds of 500 mph.
His exhaust velocity was about a mile per second. Turbojet exhausts were less than a third of that.
So from that point of view alone the first jet aircraft were way ahead of his arrangement.
He does mention an advantage over the airscrew of being able to swing the nozzle (todays thrust vectoring).