I suggest that the 'calcium oxide' which is supplied is not actually quicklime, but slaked lime. I have three reasons:
1. Quicklime is fairly dangerous stuff, and is no doubt covered by all sorts of regulations. Slaked lime is much more friendly, even available at posh builder's merchants in lime mortar.
2. Quicklime is eager to absorb moisture, so has to be in a tightly sealed container, even in the factory where it is made. When this has occurred it turns into slaked lime (hydrated calcium oxide). So why not supply the non-noxious stuff?
3. If moisture helps c-a to polymerise, there is no advantage (in this respect) in adding a compound which absorbs moisture itself.
And it may be that the resulting set product with calcium is less soluble in water than with sodium (from bicarbonate) – thus extending the usefulness of the product.
But what do I know about it, anyway?
Cheers, Tim