It is true that cliometrics have fallen somewhat out of fashion. It was quite popular into the 1980s, perhaps especially in the study of the English Industrial Revolution. A very influential book in this vein, for instance, is "The Population History of England."

And some people still rely heavily on cliometric modes of analysis in certain sub-fields of history, but I agree with you that they seem to be in economics departments more than in history departments. I think this is especially true when it comes to what is sometimes called World History—the study of how and why it came about that around the year 1500 Europeans began to see secular real GDP growth per capita whereas the rest of the world did not. Daron Acemoglu and Deirdre McCloskey both have some pretty high-profile quantitative treatments of the question, and are both in Econ departments. Scholars like Kenneth Pomeranz, Robert Marks, et al tend to use less statistically complicated forms of analysis and, non-coincidentally are in history departments as far as I can remember.

In my experience there is a certain distrust of scholars like Acemoglu and McCloskey within history departments but that's not across the board. For instance the economist HJ Voth's quant-heavy "Time and Work in England 1750–1830" has appeared in the footnotes of works by history-department historians as well as political economists.

Perhaps the most convincing argument as to WHY cliometrics came into (and then fell out of) fashion is by Timothy Shenk (link: http://www.thenation.com/article/apostles-growth/ ):

"Before 1940, no economics dissertation in the United States included the phrase “economic growth” in its title; a decade later, it was everywhere. But growth could not be studied with the same tools that economic historians had relied upon previously. People accumulate papers, and so do companies—papers that historians can later use to piece together narratives. The economy is an altogether more abstract entity, an object built out of aggregates like productivity and unemployment that can never be seen, even when their consequences are felt. Reconstructing the economy’s history required tables, graphs, models, estimates of national income and output—an entire instrumentarium that historians had little familiarity with, partly because economists had just recently conjured it into existence.

Economic history was transformed into the history of economic growth—the search for examples that preceded its breakthrough in the eighteenth century, along with explanations for why it had taken so long for growth to become routine. In the process, the field became less important to both economists and historians. Historians viewed it as the province of economists, while economists treated it as a testing ground for prefabricated models, implicitly (and sometimes explicitly) dismissing it as a refuge for number-crunchers incapable of producing the mathematically avant-garde theoretical work prized by the discipline."

It was popular for a while but fell into disrepute, though it still has some proponents and some major works still get regular citations such as 'Mammon and the Pursuit of Empire.' You are unlikely to find studies these days which rely too heavily on cliometrics, though it is still used as a component of historical analysis, it is not viewed as a the next great method analysis in history as it briefly was. History as a discipline is usually more cautious of things like cliometrics than other disciplines. I can add more on this as well as a few proper references this evening, but I'm currently away from my computer.

At my university, we have a cliometrics expert in our history department, so it isn't completely lost! I had her for an intro U.S. history course, and she incorporated that into her lesson. I also had the opportunity to take an upper division course in her main interest (American Indian history), and to do research with her, and I've only found cliometrics more fascinating after working with her.

Is cliometrics controversial? I researched a few studies in my higher level econ courses