A combination of effects with a single cause which was an immoral agency acting on the individuals in the society which led to the things you describe.
I’d point out that the plague around 300 effected the Empires enemies too.
Also, most Roman Emperors were military leaders throughout the Byzantine period all the way up till the Fall in 1453. If I understand you correctly, simply being a military leader in itself wouldn’t be problematic.
Homosexuality wasn't exclusive to the Roman empire. Empire-wide succession battles every few years were. At the inception of empire, Roman military methods were also unique, superior and unknown to the barbarians. Once the barbarians caught on and adapted, Roman victories became much more costly. Eventually, what used to be hard-fought victories became defeats. Every empire of note has run into this problem - there are ambitious men of ability outside of the empire who want to get their hands on the brass ring. The ones who figure out what to do get to become the successors to existing empires. Rome fell to superior military minds which created something out of nothing, despite Rome's ability to call on centuries of military tradition and accumulated military knowledge.