Funny you should ask that Doc.
The upfront cost of rechargeables including the charger isn't all that significant, and they do last a long time. However, that isn't the whole story. Depending on the detector, the operational life of any specific rechargeable can be as low as half that of alkaline batteries. In the case of my Garrett GTI-2500, a set of alkalines last at least 40 hours of operation. A set of fully charged NiCads last about 24 hours. A set of NiMHs about 18 to 20 hours. It isn't so much the capacity of the rechargeable batteries, but one of the voltage over time vs. discharge percentage.
Alkalines stay fairly close to their design voltage (≈1.5), until their capacity drops to about 10%. At that point, under load they drop to about 1 volt which starts to cause erratic detection. Both NiCad and NiMH will drop to 1 volt at about 40% or so of the capacity. While they can indeed be recharged, doing so in the field is a bit cumbersome.
I do use NiMH when I'm in town, but if I take a trip, I always take a supply of alkalines, and leave the rechargeables at home.