I commute on a road bike but I considered a CX bike because of a new path being completed that would help me avoid some busy freeway overpasses. The path is mostly gravel and will be good and loose for a couple of years before it is worn down and weathered enough to ride my road bike over. Right now the completed portion is round, loose pea sized gravel.
I landed on a road bike because the entry-level CX bikes at the local shop were $1500+ (not much selection either) and because I wanted to start doing 30+ mile rides regularly. But I will probably still give the path a try on the road bike once it's all connected