They also didn’t protect thier borders.
Same difference. Border management meant fighting with Goths, Gauls Vandals and Persians at locations far from Italy.
The Eastern Empire (Constantinople) made the same mistake by not throwing the Turks out of central Anatolia when they could have. So now Constantinople is Istanbul, and the Hagia Sophia is a mosque.
The price of liberty is eternal vigilance, and that doesn't mean just on home soil.