I think I agree with you about the Hayflick limit idea, but I also think it's useful to point out, as the parent does, that a sclerotic, moribund empire is probably a better place to live for the majority of people in it than not an empire, assuming there is trade and general stability.
Is it? It took a plague to launch a revolution in agriculture in Europe, leading to an increase in calories production, an expansion of human life span, and opening up an expansion in trade (which reflects an increased amount of consumption of goods beyond simple survival). The preceding periods of semi-stasis were ones of no expansion in human quality of life and punctured by the opposite when you happened to be in the wrong place during a struggle between elites.
In our concrete world: had Apple not been able to blow up the oligopoly where the phone carriers controlled what phones were available and what they could do, would we have the current explosion of software, tools, etc? In the US in particular the sclerotic phone oligopolies kept the mobile phone market at least a decade behind Europe and Japan.
This is exactly the issue I'm talking about. It's very plausible that the world got much better after the plague, and that the plague was an important catalyst. But it also seems obviously true that absolutely no one alive at the time would choose the plague in order to cause that improvement.
Not sure why that is particularly strange. In the age of overt empire, Gibbon wrote an explicitly cautionary tale, like the momento mori that accompanied a triumph. But we aren't in that same age.
From a broader perspective, the nature of "structural" Rome, especially once Octavian (Augustus) took control, lead to sclerosis as the control and wealth and power overwhelmed other activities of state and society. For example the literature of the republic and early empire is greater than that of later periods not because people became dumber but because society, even if richer over all, could not afford it.
Arguably the empire continued, not just in the east but through what remains of Charlemagne's realm (more diffuse yet of greater scope): hundreds of millions of people speak a form of Latin (we call it Spanish or French or other names); many legal systems contain roman influences (though sometimes vestigial, with a legislative chamber called a "Senate"), and many cultural norms trace back to or through Roman times.
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You can see this today, writ small (I'll ignore the politics of the larger scope). The older megacorps (think US Chamber of Commerce members) are focused more on extraction (of rents or of re-mining the same seams) rather than customer benefit. The "newer" (only a few decades old) tech upstarts themselves have largely entered late middle age and are heading to the same fate. Google, once an admirable innovator, is regularly pilloried on this site for having lost its way; some companies required a near death experience (Apple) or spell of privation (Microsoft, IBM) which may help (MS) or may not (IBM). Even in the old guard, GE is haeding downward, and though they've been around for a while and have in the past been a force for good, will anyone mourn?
I've long believed there's a Hayflick limit for both companies and social systems. And as it is for humans, it's a good thing.