Add a recipe of some kine to combine any divining rod with a pick to give the pick the same functionality; similar to an enchant.

Isn't it enough that you can hold them in your off hand and a pick in your main hand?

I generally mine with a pick and torches or a shield depending on how dangerous mobs are. The divining rod is one more switch that can be the difference between death or not. If not combining with picks, perhaps lengthening the time ores are displayed a bit so one does not have to keep it in hand as much.

maybe a divining rod helmet? craft with the rod to use and you can uncraft to separate them?