Eye-colour is a genetic trait, inherited variation. It may be used together with other genetic traits for population-genetic calculations, it may also tell us something about selection over time. And, if genetically retrieved, what someone looked like. It is one genetic trait (or actually, a few), with its own history, and its own demography, and will not reveal much about a population on its own. It is just that, nothing more. In most contexts it is not good or bad to express one type of pigmentation in the iris, it does not define a group, or the history of a group (for that you need many many more markers, and also some kind of reasonable definition of the group). There may be scientific questions related to eye-pigmentation that are interesting, but in the same sense that there may be specific scientific questions for any and every genetic piece of variation.
There is a public interest, however, and this should not be diminished. It is interesting, from an entertaining and general-curiosity point of view, to know what people looked like. Within our ATLAS-work, we have helped museums retrieve information for reconstructions (the Viking at the newly opened museum Vikingaliv for example), and also talked about various aspects on demographic paths for this specific trait in popular-science reportings (last evening in Vetenskapens Värld for example). For example, if we relied only on eye-pigmentation from the one Viking at the Vikingaliv museum, we would conclude that the Vikings had their origin among southern, or southwestern hunter-gatherers before the first farmers came to Europe. But when we look at a larger number of markers in people that lived in Scandinavia 1000 years ago (a more easily defined group than ”The Vikings”), we conclude that they are a genetic mosaic with traits from southwestern Europe, Anatolia, the Steppe, and many many more places over the millenias. Nevertheless, it is fun to know what one person you could meet on the streets of Sigtuna some 1000 years ago looked like. So, if I started by quoting an old song by The Leathernun, I´ll end it with an equally old quote from The Pogues: So a roving I go, for a pair of brown eyes.