This statement is the one I hear most often from new parents when discussing the need to childproof. When I first became a parent, I had the same misconception. I thought nothing will happen to my son because he won't be out of my sight. It's most definitely easy to always watch your baby before they learn to walk, much less run. Ask the parents of a very active toddler if they always watch their baby. They can tell you it's nearly impossible to keep up with them.
Most new parents don't realize how quickly a child can get out of their sight. That is the main reason for childproofing, to prevent injury from accidents in the home. Children are going to explore, be inquisitive, and get into things. Our job as parents is to give them a safe environment in which to learn and grow. Taking the steps to keep them safe at home before they become mobile is the single most important thing you can do to prevent accidental injury.
The other major factor in childproofing your home is identifying the risks. When I do a Home Safety Evaluation, my main focus is on educating my client on the things I look for. Having a fresh set of eyes to look at your home and point out the hazards is invaluable in creating a safer environment for your child.