That is true of many barbarian tribes, but not all. Many Germanic and Gothic tribes were more hostile than friendly to the Roman Empire for most of its existence. Rome was sacked by Visigoths in 410.
The sacking of Rome by the Visigoths was not official policy.
Alaric didn’t give his permission. His troops were hungry for loot and just went and did it.
The serious sacking came later, in 455, with Geiseric the Vandal in charge. Now, THAT was a party!
Read your history.