He was very invested in Italy, having married into Gothic nobility, and was actually popular among them. But the Goths were not the problem, it was that Italy was not a self sustaining conquest in the short term, while resources were needed in the eastern border.
A careful balance could be held to, well, hold both Italy and the frontier, but unless the Persia is truly vanquished to an extent were all or most resources can be redirected towards a defense of Italy, it would fall as soon as the next germanic tribe desires to cross the Alps.
A possibility would be to somehow delay any invasions from the north through more effective diplomacy... But that kind of is what they did IOTL, and it more or less was directly responsible for the Lombard invasion. See, there was an east German tribe called the Gepids, who had settled in the Pannonian planes, and were putting pressure on the Roman frontier cities of the Danube, so they sponsored another tribe, the Lombards, to kick them out. They eventually migrated further west, to Dalmatia, and when they sensed weakness in Italy, they invaded. So, I'm not sure if "better diplomacy" is so much the key rather than "luckier diplomacy".