The truth is that you don't. All that's required for almost any training run is a pair of shoes[*]. Everything else is an extra; it's up to you to decide whether each of those extras is worth carrying.

[*] That's true where I live (northern Europe) for pretty much all of my runs up to ~20km. In hotter or sunnier climates it may be necessary to carry water for shorter runs and/or put on sunscreen.