The problem here is a lot of what is being said is true. There is not one answer to the original question, which in turn is rather artificial.
It is true you need a compressor otherwise you haven't got a jet engine; all you've got is an oil fire. Also higher compression tends to lead to more fuel being consumed. However the point of compressors is to raise pressure. The thermodynamic efficiency of internal combustion engines increases with pressure and temperature. The explanations given above may be true; it doesn't really matter. All you need to know is you want to get the pressure as high as you can without suffering from side effects like spontaneous combustion/explosion.
Note that pressure is not the same as compression ratio. That's why superchargers and turbochargers raise pressure - they help stop brake mean effective pressure falling as rotational speed increases or air thins.