I think it more likely that their ability to smelt iron was undeveloped enough that while they could smelt small pieces as decorative curiosities, they could not smelt the larger pieces needed to make tools, weapons, or armor, possibly either practically or economically.So, apparently we have carbon steel fragments (likely for jewelry) dating from circa 1800 BC from Kaman-Kalehöyük in Turkey, which means that the people DID in fact have the capacity to work iron at the time. The question is therefore not as much about being able to (we know that they were, at least in some places), but applying this smelting capability to tools and weapons instead of decorative items. Is it possible that the use of bronze was just so institutionalized by this time that groundbreaking advances in metallurgy would have threatened a cultural elite?
Consider, for instance, Albidoom's comment about aluminum. It was possible, but expensive and difficult, to smelt aluminum until the invention of the Hall-Héroult process. For this reason, the main uses of aluminum until then were in decorative applications, much like the iron you mention being used in jewelry. Of course, we know now that it has many other applications besides, but it would be useless to ask whether it was possible for the people of, say, 1850 to "apply their smelting capacity to tools and weapons," because their smelting capabilities weren't able to produce sufficient quantities at a sufficiently low price for that kind of application. The same was probably true of whoever made the jewelry you mention with regards to iron.
(Not to mention, as Analytical Engine did, that bronzes are better than early irons in a lot of applications...the latter is just cheaper if you have a developed smelting capability)