Both the Western and Eastern Roman Empires fell by losing conventional military campaigns.
That is a pretty narrow view. Both were overwhelmed by barbarian hordes who did not value or respect the level of civilization, after hundreds of years of contact. You seems to think that some level of appeasement would have changed that. But I do not think so. When cultures that are generally compatible share borders they become more and more alike through contact. However, some cultures are not compatible. Like oil and water, they don't mix. Only if you just look at policies right before the end would you try to make the argument you are making. Think your way back to Julius Caesar, Omnia Gallia in tres partes divisa est.