You could. Many or most places do that. But US recipes typically don't, and work out fine. So I guess volumetric measurements that assume default packing conditions often work out OK in practice, though @lostlogin above reports a corner case that doesn't work.
Most people don't sift out the chaff or rocks today, but sifting performs important functions of making flour lighter for certain "light & airy" recipes that cannot be properly performed only by weighing.
Your prior point was that you don't need to sift flour but only weigh it. That is false, as sifting flour changes the properties of the final baked product. You now changed that to, in essence, say that weighing tells you the weight of flour. Yes, weighing tells you the weight of what is being weighed.
In this case, the forms of the statement are identical. "One cup of sifted flour" is semantically identical with "sift one cup of flour."
The difference is the method of measurement, whether by volume or by weight. Then, it is important to either understand the rules of recipe specification, especially with baking, or to have the recipe specify as to whether there are implicit steps.
