I have an Australian-made ReZap Battery Doctor that charges alkalines.
It works - it really does.
However, there are four caveats:
1) It cannot bring a completely flat alkaline back to life. With shallow DoD and frequent charges it works well.
2) Not all brands of alkalines take a recharge - and there's no picking which cell will take a charge.
3) Recharged alkalines are only suited to medium-low drain applications, unlike the first time. Definitely no hotwire use!
4) Only 20 or so recharges are possible with a good cell.
It also recharges NiCad, NIMH and "RAM" cells (e.g. Grandcell), and internet research told me that an earlier model of the ReZap actually charged carbon-zinc cells, but they stopped this.
And, yes Virginia, you CAN recharge Carbon-Zinc cells. Flat-pile layer-built dry cells respond better to trickling than cylindrical cells, which is why 1950s AC/DC & 3-way valve radios often had a "reactivate" setting where the batteries could be "reactivated" (i.e trickle charged). With careful and judicious use of this feature, you could double the service life of your (very, very expensive) B battery.