"Post-marinating"? Is it a real term or do my taste buds deceive me?
There are several reasons why you should marinate before cooking:


Many marinades contain raw ingredients that should be cooked along with the food being marinated, such as garlic or ginger.  In some cases this may actually be a health hazard (raw garlic can harbor botulism), in other cases you'll simply end up with an undesirable pungent flavour.
Many marinades also use some amount of acid, which helps to kick-start the process of breaking down the connective tissue and tenderizing the meat.  This is an especially big deal for chicken breast meat and tougher cuts of beef or pork, because most cooking methods (except for slow-cooking) don't do much of this and tend to produce a tougher, chewier end result.  Once the meat has already been cooked, using an acid-based marinade won't give you much more tenderization; you need the combination of acid and heat.
Finally, many spices release most of their flavour when heated (cooked).  Examples are cinnamon, saffron, star anise, and various types of hot pepper or chili powder.  If you marinate after cooking, you won't get much flavour from these.


Of course if you are using a very simple marinade such as soy sauce and are marinating only for flavour purposes, then it might not matter much, but that's the exception rather than the rule.  Marinating afterward can certainly improve the taste, but most of the time you'll end up with better results by marinating beforehand.