ston, look at it this way...
Yes, you (and your listeners) ultimately control loudness with the volume control. But let's say you aren't consistent with the volume you mix at. Maybe during the day you like it cranked but have to do it quieter at night to avoid problems with the neighbors.
Because of the equal-loudness curves batsbrew alludes to above, you perceive sound differently at different volumes, a phenomenon that will unconsciously affect all your mixing decisions. You'll end up with inconsistent mixes: too much bass in some, not enough in others; a tendency to over-compress some things and under-compress others; lost vocals, oppressive kicks, harsh guitars; mixes that don't translate well from one system to the next. Mixes that sound good loud but fall apart at low volume.
These can only be avoided by mixing and mastering at a consistent volume, and by correlating meter readings to what things are supposed to sound like -
at that volume. That's where the calibration comes in. Once you've established a known relationship between meter readings and speaker volume, you are then free to turn the speakers up or down, knowing that you can still rely on the meters as a sanity check.
The inspiration for the K-system was a previous loudness standard that had been in place for decades for motion picture exhibition. It assures that a movie's sound will be consistent from one venue to the next. Just as you want your music to be in the same ballpark as commercial offerings heard on iPods and radio, as well as being internally consistent within a collection on a CD.
You can certainly get there without the K-system or R128, and it was done that way for many years. These standards are just conveniences to get you there with less trial-and-error and greater consistency.