Question

why is the cell cycle important

Answer 1

(not my work)

The cell cycle is necessary for a cell to divide (by mitosis)
without that we would never have grown from a single cell (zygote) since that zygote cannot divide without cell cycle.

It is also necessary for repoduction (producing sperm or eggs [gametes])

For healing broken tissue

growth and development

and the body actually have ways of interrupting the cell cycle in cells that are malfunctioning, it is called programmed cell death (aka apoptosis). This helps stop a lot of cancerous cells before they can become malignant.