Because it takes a lot of fodder heroes to level up 4* and 5* heroes, and we can’t stockpile fodder heroes. If we don’t have any 4* and 5* heroes worth levelling, then we should stockpile food and recruits, so that when a good candidate for levelling does appear, that food and those recruits can be converted to fodder and the new hero levelled.
For food storage purposes only, TC13 is just fine - it’s no worse than TC20 and also no better. But remember: the reason we might want to store food is because we lack a suitable candidate 4* or 5* hero to level. Our best chance of collecting a good candidate is by running TC20, not TC13. For a similar cost, every time TC13 trains a hero we have only about a 5% chance it is a 4* hero; every time TC20 trains a hero there is a 20% chance it is 4* and an additional 5% chance it is 5*.
So once one has a TC20, why would one ever use TC13? You would use it if you really need to deepen your bench of 3* heroes (TC20 will help with this as well, but you might want multiple camps doing it). Otherwise, it’s a terribly inefficient use of resources relative to TC20, and if you had excessive food you would never have any reason to put it in TC13 - it should always go to TC20.