A company may set prices any way they like – there are no rules!
However although they will consider costs, they will also consider competitors and the effect of price on the demand (as I explain in my lectures on pricing).
They may decide to set the price by adding a mark-up to the cost, in which case they would be better using ABC, but it is there choice – there is nothing to stop them using traditional costing. However they certainly can use ABC (and would be better doing so).