Hi orda,
I see what you are saying. The US cannot really afford its military, in the same way that the Romans couldn't. I agree.
But the details are fairly different.
Simply, third century Roman emperors paid their armies extravagantly in order to support them in their civil wars.
That's a bit different from not funding foreign wars in places like Iraq.
Also, I don't see the same issue of legitimacy and authority in the US. Democracy is a much better system than Roman imperialism in terms of avoiding the issues surrounding hereditary succession. If they had had a peaceful method of replacing bad emperors, I suspect Rome would have lasted a lot longer than it did.
There were other issues of course. Following Julian, Gibbon thought that Christianity undermined the martial virtues of ancient Rome. I agree with the professor that the Roman authorities could have used a more coherent financial system. Best thing they could have done was to get a central bank, introduce a fiat currency, lock up the gold in the Castello Sant'Angelo and outlaw slavery (inefficient system).