Yes, there are reasons that a public health insurance option is a good idea. Most significantly, people with pre-existing conditions or who are otherwise high risk need a way to obtain health insurance and health care. This is not viable to business because they do not stand to make a profit. This is where the government can step in and provide these people a valid service that promotes their health.
There is generally no use for a public option for health insurance, as it is the least useful form of health insurance. Because a public option would be supported by government subsidies and tax dollars, it would always be either taking funds from people who don't use the system, or be under funded, as private insurance is always better and preferable to government insurance when it can be afforded. A public option is not a good idea.