Why cooked food considered nutritious if proteins decompose at much lower temperatures?
Cooking is just a form of digestion.


  What is digestion?


Digestion is the process of breaking down big molecules into smaller molecules. When you cook food you break down big molecules into its small components.


  Why do we digest food?


Think about a long sequence of DNA for example. You eat corn and you have in your body a long sequence of corn DNA. What can you do with that long molecule....well, nothing. You need to break this long molecule down in order to be able to assimilate the constitutive nutrients. With those nutrients, you can now make up your own DNA. In other words, we need to break the big Lego castle that is food to get the building blocks in order to rebuild a spaceship. Digestion refer to the first process (breaking up the Lego castle). We refer to the part of the metabolism who breaks things down as catabolism and we refer to the part of metabolism that build things up as anabolism. Note that catabolism + anabolism = metabolism.


  Why do we cook then instead of digesting by ourself


Digestion takes much energy and require the organism to have the right organs and to have the right matter (enzymes and stuff). We can save up energy (and the other stuff) by digesting the food outside our body. One could say that humans, (just like spiders for example) are performing external digestion.


  Why cooked food considered nutritious


Cooked food don't have more nutrients than raw food. It is actually likely that in the process of cooking you would lose some nutrients going in the water that you throw away typically.

The big difference is that nutrients in cooked food are easy to assimilate which might end up being more healthy depending on the specific food source. Cooking may also destroy potentially toxic products.

Note that in response to the cooking behaviour, human gut has evolved to be shorter than it was in our ancestor.