I watched some cooking videos and sometimes I see that in order for the pepper, salt, sake, or whatever go into the meat, the meat needs to be put in the fridge, even for 30 minutes. Why is that? Is there any reason it needs to be put in the fridge?
For a 30 min marinade, no, you don't have to put it in the fridge. In fact, many recipes will call for removing thick beef cuts from the fridge 20-60 min before cooking, to let the meat come up to room temperature.
That being said, there has been some testing of what sort of difference bringing a steak to room temperature makes, and the general concensus is that cooking a cold steak gives better results. America's Test Kitchen's tests found that people preferred frozen steaks, although it required freezing to ensure you didn't develop surface ice crystals, and cooking in more oil than typical.
Food safety. Leaving meat around at room temperature is never a good idea. Two hours is the USDA recommended limit for the whole 'lifetime' of the meat.
It makes little or no difference to the flavour absorption.
In order to put the decomposition process on hold you need to put the meat in the fridge.