Dog-eared means that a corner got folded down (making a diagonal) on a page as a bookmark. A dog-eared book isn’t necessarily beat-up beyond the damage to the corners of pages. Catty-cornered or kitty-cornered is adjacent to something on the diagonal, i.e. not orthogonally next to it like up, down, left, or right. So there is an argument to be made for a loose (coincidental) connection between those ideas, but I don’t think they come from the same roots.
Pancake mix in particular benefits from the large scales at which the pre-mixed stuff is made. Measuring out those smaller proportions of dry powders precisely and accurately is much more difficult at home even if you opt for using a scale instead of measuring cups. Just read the ingredients list to avoid the brands that may include the extra binders and other ingredients you want to avoid.