Originally Posted by QJB
but fundamentally the reason seems to be to increase the overall efficiency of the engine.
No.
Fundamentally, the reason is that you need a pressure differential for extracting work from heat. And since there is no pressure increase in the combustion chamber of a turbine (turbine = open flow engine), the pressure increase must be created by a compressor.
Without a compressor, there no work that can be extracted !
Luc