Jet engines have several advantages vs. piston-engined A/C, apart from ability to propel aircraft easily above 450-500 mph. No need for a propeller, no reduction gearing, no need for elaborate cooling and intercooler arangements. No 'power boosters', like ADI or GM1. All of this affords for a light and straightforward installation of the engine. It also allows for a simple operation of engine. In words of John Grierson, from
Wikipedia:
"The main impressions of my first jet-propelled flight were first of the simplicity of operation. The throttle was the only engine control; there were no mixture or propeller levers, supercharger or cooling-gill controls and the fuel system had simply one low-pressure valve between the tank and the engine pump, and one high-pressure valve between the pump and the engine. There was no electric booster pump. Secondly the absence of vibration or the sensation of effort being transmitted to the pilot's seat was outstanding."
Add in no torque to fight against at low speeds, the simplicity alone would've made it much easier for the novice pilots to master flying of a jet aircraft. From German point of wiev, ability of the jet engine to use diesel fuel is very interesting, too. Diesel fuel is also much less flamable than hi-oct gasoline.
Armament installation is also easier since there is no prop turning at the nose.
Granted, not everyting was rosy - fuel consumption is/was very high, so logistical efforts need to doubled vs. piston-engined fighters of the LW; throttle needs to be judicuously applied so engine does not shut down, wings need to be well outfitted with high-lift devices to help with take-off.