The last five emperors of Rome were all homos.
The social decline of Rome is well documented.
It is not silly.
Possibly true.
However, you should list the unnamed five last emperors, not Nero and Caligula.
It is as if I were to point out the homo-ness of James I as the “cause” of the present decline of the UK. The timespan involved is similar. Yet everybody recognizes today that the sexual preference of James is pretty irrelevant to anything happening today.
For about the last 75 years or so of the Empire, who was Emperor and who he preferred to bed were remarkably irrelevant, as the Emperors were merely figureheads for military commanders and barbarian chieftains.
Are you aware Constantine (died 337, over 150 years before the Fall) made sodomy a capital crime? What is your evidence the late Roman Empire was overrun with homos?