More than having a wide horizon of applications in the real world, it acts as a powerful lens to see through a problem. It helps us decide if a problem is solvable or not. If yes, then how, how fast and how accurate? If not, then an algorithm again helps us decide, if we can solve a part of it.

Talking about why we should use algorithms in programming, we must understand that computer programs adopt different algorithms run on computer hardware which has a processor & memory and these components have limitations. A processor is not infinitely fast and the memory we have is not free. They are bounded resources. They must be used wisely and a good algorithm that is efficient in terms of time complexities and space complexities will help you do so.