Why do battery chargers work on even numbers of batteries?
In a word... Simplicity.

The chargers you refer to will charge pairs of batteries in series, rather then all batteries using individual charge circuits. This simplifies construction, component count, size and cost.

They cannot usually employ parallel as otherwise if batteries of different charge levels were inserted at the same time, you would have the least charged cell take the majority of current until they became balanced, and this could be unsafe or damage cells.

Its also easier to produce circuit that provides 2.4V charge voltage than 1.2V, since the losses in the switching for the circuit would be less of a concern, and the components are likely to cost less in this case.