We're not reciting the past, we're uncovering the past and interpreting it as well as teaching others how to do the same. Just because we can't predict the next big thing doesn't mean we're irrelevant - rather like seismology isn't irrelevant because it can't tell you when the next earthquake will happen on this or that fault line.
Historians tend to say "You're cherry-picking your data" when the cliometricians or cliodynamists come to town. They're taking material from one set of circumstances and missing another, conflating events that aren't equivalent or sometimes simply misreading things that have changed dramatically over time. (Did you know that up until the 19th century in Europe, it was an established belief that women were sexually insatiable and utterly physical creatures, incapable of ruling their baser emotions while men were more spiritual and disinterested in sexual or physical matters. Nowadays, of course, western societies pretty much put it the other way around. But if you read something about woman's 'nature' in a fifteenth century source, it's coming from a wildly different assumption than a 21st century individual might expect. The same kind of 'false friends' exist in everything from laws to agricultural practice to religious activity. Nothing stays the same, even when people are trying to conserve practices!)
Historians also tend to emphasize how behaviours are socially constructed and how those constructions change over time. So, for us, to expect that the same rule would hold for 1830 and 1930 and 2030 is hard to believe. Furthermore, that it would hold for all societies in some cycle of development? Again, tough to swallow. I've looked at some of the material they're putting forward and it's not rocking my world yet, nor is it making a big impact with other historians even though Turchin's book has been out for years, now.
With regard to Turchin, Dewey & Kondratiev and their long-cycle models, I'd have to say that most historians would be with the doubters. Not enough's attributed to human agency as matters are described to cycle up and down in response to "natural laws". Never underestimate the power of a few well-placed individuals to screw everything up at unpredictable moments!
It's not inevitability, it's incidence. Social, technological or political change takes a long time to shake out. While we can talk about patterns, it's never a good idea to believe they're natural forces dictating the future. Instead, we'd talk about patterns in terms of parallels: see, when the printing press was developed and popularized, these are some of the effects that it had, direct and indirect. How can that inform our understanding of how the internet is changing modern economies, culture and education, say? But nobody who tells me something like, see, it took seventy years from the advent of printing in Germany for Luther's 95 theses to be circulated, so there's a cycle for you!, is going to convince me they have a useful scheme. I'd say that such pie-in-the-sky claims are counterproductive.
Turchin hasn't engaged historians nearly as much as he has economists and his interest in predictive modelling fits more in with that field than with history and historians whose chief interest remains in accurately documenting the past as opposed to thinking we can predict the future. That didn't work so well for Fukuyama
, now, did it?