“Exercise” is just an integral part of life, like eating and sleeping. Just because it can’t be reductionistically understood doesn’t mean it’s not necessary.
That’s one reason. The other one is that when you have a small amount of total milk, you have to make sure there’s enough for everyone. By pouring milk first you can more easily measure how much milk you pour per cup.
Taylor series work on differentiable intervals. You specifically chose a function and interval where this is not true. Of course it will not be a good approximation.