After the war, the Jumo, designated the RD-10, was used in Russian jets, such as with the Yak-15, Yak-17, and SU- 9. The Jumo 004 also influenced the French, who used the Jumo 004 in the Arsenal VG.70, and the Sud-Ouest S.O.6000 Triton. aircraft.
Doesn't that list tell you something?
Where are the really successfull planes? The Mig 15s, the Sabres etc?
Another engine, He S 11, was designed for 1300 kg thrust, which was after very big diffuculties achieved in 1944. They had major problems with creating some "diagonal wheel", hell if I know how to translate that. "But then it was the most powerful German jet engine - but too late. Only the Americans who captured the Zuffenhausen factory built a large numbers of that jet engine in my (Heinkel's) factories for test purposes."
The RR Nene, that powered the Mig 15, was bench tested in 1944 at 2,270kg thrust. It was produced in huge number in the Soviet Union, and China continued producing it until 1979.
Germany undoubtedly had a lead in jet aircraft design, but they were behind in engine design.
First Jumo 004-engines had 88kg of nickel in them. When they started serial production amount of nickel was dropped to 24,4kg (27,7%) due to war-economic reasons. Because of this Jumo's operational life lasted (at best) 8-10 hours. This and other sortages in raw materials also caused lot of flame outs and engine fires.
It's a simple fact that most of the problems with Jumo-engines were due to lack of proper raw materials.
The first Jumos, with 88kg of nickel, were never intended as production engines. They were very heavy, and even the production 004B was too heavy at 720kg. For comparison, the RR Derwent was 420kg, and the much more powerfull Goblin (1,300kg thrust) weighed 680kg.
Hell, X-1 was based on a German design
Ever seen the earlier Miles M.52?
Germans had better engines ready to go into production, but why settle for them - US, Britain and Soviets instead brought over a flood of German engineers and scientists instead, and used them to design even better engines, planes and so on.
Which post-war engines were based on German designs?
Aircraft yes, Germany had a huge lead, but not in engine production.