"If this knowledge is valuable, the best way to show a support for it is hiring somebody to work full time on this problem."

Why not have both? I.e. academics and students dedicated to the fairly monastic career of being a professional historian (which I am), but also prizes which seek to bring in experts from other fields with different skillsets who may approach the problem in an original way.

Obviously there is a limited amount of funding for anything. But surely some of the billions being donated every year to the general funds of elite universities like Harvard would be better spent setting up specific, goal-oriented prizes modeled on the Vesuvius Challenge.