Question

German conquered west Rome, why did they fail to inherit the roman achievement and rule west rome?

Answer 1

The Germanic tribes that took over the Roman Empire territory in the west had a history as tribal and hunting/agricultural societies.   Even in times when it was fracturing in many ways, the Roman Empire was built around central organization and governance.  The Germanic tribes had been more loyal to their own tribal groups than they were confederated into a unity with one another.  Their historical patterns of development also had been more built around hunting and farming.  They were not as developed in coordinating government over a massive stretch of territory.  The Germans had begun learning things from the Romans during the years when many of them served as mercenaries in Roman armies.  And they would learn more about building a far-reaching system of government.  They were not ignorant "barbarians" when they took over Roman territory, but they weren't united in a plan to govern the region as a unit the way Rome had.

For comparison, you might think of the difference between the Native American nations that existed in North America when settlers from Europe came and took over their territory.  In that case, the situation was reversed. The native tribal nations were used to operating independently as their own tribal nations, and were focused largely on hunting and agriculture. The white settlers were aiming at building a society more similar to how Rome had operated.