You would be surprised (or perhaps maybe not) at how many people who work in this field actually have, or had, experience with mental health issues. Or trauma. Etc. When I was hospitalized, I met two other counselors and a social worker who were also in the hospital. It wasn't the job that put them there, they sought the job because of what they had gone through. It tends to give us more insight. And, like ElsaMars mentioned, many clients seem to appreciate that more, having someone who has been there. Who gets it.
One struggle that you may find is that there are cases that will get to you. Some cases can be so mentally draining, and so it is incredibly important to make sure that you don't forget to take care of yourself because it can be very easy to get lost in this type of work.