The cell cycle is part of life, so there would be no life as we know it without the cell cycle. Everything alive is made of cells, and they all divide to make daughter cells. If cells didn't divide, they'd just get bigger until they got so big that they fell apart.

Before the beginning of life, scientist think there were collections of molecules similar to some of the ones in cells. Somehow those molecules joined together to make bigger molecules, with the help of some energy source such as solar energy. The bigger molecules arranged and rearranged and combined to form even more complicated collections of molecules, with the help of energy. When complicated collections of molecules form, they often can do new things that the separate molecules can't do. For example, there are protein molecules that come together and make little tubes. This kind of thing happened over and over again in different ways to create the life we have on earth. But before the cell cycle, there wasn't life as we know it.

If the cell cycle doesn't take place for a single cell, that cell will not reproduce. This is normal for certain types of cells, especially neurons. But it is a problem for most other types of cells, for example, skin cells. These usually reproduce constantly to protect the organism from damage, normal wear and tear, and to ensure it is still protected as it grows. I think the most general way to think about your question is this: every cell that reproduces does so for a reason, usually to help an organism grow. If those cells cannot reproduce, it will probably harm the organism in some way. (The exception is cancerous cells, which reproduce without serving a purpose to the organism.)