My college coach, who is still active for my DI alma mater never ran distance in college but has coached XC for nearly 30 years.
But it is tough and things have changed. In order to get a decent paid position, without coaching experience, you usually have to be a former elite with name recognition.
For the rest of us in order to get a DI, DII or DIII job you have to volunteer at that level for a few years and work up to an entry level $25-35K position. It is tough to be taken seriously as a volunteer without having personal experience to draw back on.
The other route would be high school or JUCO coaching and trying to work up. You have to really stand out at those levels to move up though. For the most part a school will fill a vacant position with a DI volunteer rather than take a chance on a high school or JUCO coach, or even a lower division coach.
A recent example from my region fo the country, Missouri Kansas City lost James Butler to New Mexico this past summer. Since I have not seen a posting for the position my guess is they tabbed their current distance volunteer for what is probably a $35k job in Kansas City. It does not pay great, but if they had opened it up they would have gotten some good young Jayhawk conference coaches or some young KC high school coaches to apply. Instead they went with what they knew. I do not know Brent Gummer, or whatever his name is, and I am not saying that UMKC made a bad hire, time will tell. But the above scenario is the way a lot of schools go with track coaching positions.
Regardless of competitive experience the best way to land a coaching job is volunteer at a competitive DI school. After a few years it does not matter what you did as an athlete, your record speaks for itself. A lot of great coaches were mediocre athletes. But if you are 25 years old, and are a passionate about track, but you never broke 15 minutes in a 5k you will have a tough time getting athletes or other coaches to take you seriously.