I see the same old matras about 'it doesn't cost anything' have been trotted out again, as if it were written on a stone tablet somewhere.
Which of course, is highly unlikely. Until someone provides numbers, I will remain unconvinced.
This derives from microeconomic models, and common sense. This is pretty basic stuff taught in business school. You can peruse textbooks and journals to find specific examples: the Harvard Business Review used to be a good source, and case-study books are helpful as well.
In typical products, you have a fixed, upfront, or development cost, which is everything a company spends before the product even before it hits the market, which includes market research, design, engineering, finding suppliers and distributors, and setting up manufacturing. As mentioned by the OP, adding video to a still camera truly does add costs.
But then we also have marginal unit costs, which is the cost of producing each item, along with ongoing administrative and marketing costs, and as mentioned, video features add to unit costs as well.
The total cost per unit however, is the marginal unit cost, plus the fixed cost
divided by the number of units made. The total cost goes down with increasing production run, and as total units made increases indefinitely, the relative fraction due to fixed costs goes to zero, which leads companies to deliver products with large unit volumes. And with large volumes, you can get economies of scale, where the marginal unit costs go down, with increased automation, favorable supply contracts, etc,
Then we come to supply and demand analysis. With the vast majority of products, potential buyers will be more prone to buy something if its price is both low enough and if the product better meets their needs, and considering the costs of manufacturer, and the competitive environment, a certain number of sales will be made.
Suppose a manufacturer decides to make two models instead of one, a video-only model and a stills-photography-only model. The upfront costs would be higher since they are dealing with two products, while the volume of either are going to be less than the single hybrid model; and so the total cost of either models will have to be higher as total costs are higher. But this does not take into consideration that some folks want to do both, and aren't willing to pay twice to get the same functionality, and so they might decide to buy a competitor's model which can do both stills and video, and so the price goes up even more for the dedicated stills and dedicated video models as demand falls.
Canon makes dedicated video models, and they cost a fortune. Nikon decided to make a dedicated stills camera, and it is rather expensive compared to hybrid models: and interviews of Nikon executives indicate that they consider that product to be a failure—while they can recover unit costs, and so the model is still sold, they will probably not recover their fixed costs.
