One of my favorite dessert recipes is Dorie Greenspan's French Apple Cake. It calls for "4 large apples". The recipe is equally enjoyable with a wide range of apple mass, but the character is definitely changed depending on what you do. I think baking is a lot more flexible than most folks give it credit for, but getting more precise units helps ensure consistency from cook to cook and from batch to batch.

For reference a friend who'd expatriated to the midwest posted something about some giant apples they bought. I replied with a picture of an average apple I bought, roughly twice the size of theirs.

  Meanwhile, the "cup" measurement can vary depending on the order of which you
  put the apricots into the cup - do you put the smallest fruit in first, or
  the biggest?

Yep, some recipes don't require precision, but something like a soufflé might.

Weighing things out is the correct method. What could be useful is if recipes provided the ratios of the ingredients along with error margins, so that you could easily type in an amount (e.g. 100g flour) and it'd scale the other ingredients to match. However, maybe that's overthinking it.