In fact, after the war the USSR has briefly reconstituted the manufacturing of V-2 in Germany, employing thousands of people, before transplanting this entire industry to the USSR. This dramatically lifted the level of Soviet manufacturing and relevant metallurgy.
von Braun's dissertation was on engine design and testing. But when he built the Redstone missile in the USA, he ordered the engine from a US company -- the engine which was already a generation ahead, compared to the imported German engines which the US engineers studied after the war.
Meanwhile, the Soviets have developed even better engines, completely on their own, though with the important parts built using the materials and the equipment brought from Germany.
So it is debatable whether having the German higher-ups and having a greater continuity with German design philosophy was a good thing or a liability.
It is less well known, but France have also imported a significant number of ex-Peenemunde engineers for their program. And their engines developed in a way different from both the American ones and the Soviet ones -- which definitively shows that although internalizing the German know-how was the starting point for everyone, it did not define the path of subsequent development.
Of course, the engines were not the whole story. The Germans took to the USA the advanced prototypes of the inertial guidance systems which were developed for the missiles that were supposed to come after the V-2. And the Soviets got Helmut Gröttrup. This did have its effects in both cases.
I don't know why this WW2 rocket discussion happened to begin with, but people here don't seem to understand that there is no magical inherent technical skill which is unique and irreplaceable. Experience helps to speed things up, sure, but it can be acquired by any program given time and resources, with no talent blockers.
That's a bit oversimplified. The Russians got quite a few important scientists and engineers in other areas (aircraft design, nuclear physics, electronics, radar, optics), they just didn't make as good use of them as the US (e.g. the 'American Germans' essentially won the space race for the US).