As far as I understand, baking powder is basically just baking soda (sodium bicarbonate) combined with an acid.

Also as far as I understand, cream of tartar is a common acid in baking powder - and also a common ingredient to stabilize egg whites in a meringue, so a lot of people already have cream of tartar on hand.

So is there any difference between using single-acting baking powder and just adding some cream of tartar along with baking soda? In other words, should replacing baking powder with baking soda and cream of tartar have much of an effect on the final product?

To me, this feels just like brown sugar versus white sugar + molasses. Most people buy brown sugar, but have molasses for specific recipes anyways. In the end, it's far more practical and also cheaper to just do white sugar and molasses instead of keeping white sugar, brown sugar and molasses in stock all the time.