I don't think they were relevant in the past either. The British empire may have been similar to the Spanish or Dutch and followed a similar path. These were maritime trade empires in the age of discovery, monopolizing new trade routes.

But, I don't think the Ottoman, Chinese, Arab, Hitite empires give us any predictive information for the longevity of the later ones.

I mean, history does show pretty convincingly that "stuff ends" eventually. It's got some examples for how, they are usually fairly specific and unclear. Europe has been obsessively theorizing about The Fall of Rome for 1500 years. All those musings really tell us about is the people doing the musings. It was because of Debauchery, Christianity, Tyranny, Civil Strife, Monetary Policy, Cultural Purity, Military Discipline etc. etc. depending on who you are.

I bet you can guess that Victorians suspected orgiastic debauchery while Marxists suspected class structure.