It's actually been close to 15 or 20 years -- can't remember the exact year -- since the NCAA quit bringing the other divisions into the D-I touranment. Many smaller schools (Clarion, Lehigh, Edinboro, Millersville, etc.) opted to move up to D-I to continue to compete but the other divisions have not gone to the big show since the mid-to-late 80s.
I was at Northern Iowa in the mid-to-late 1970s when the Panthers won a couple of D-II national championships. It was exciting to watch the guys win the D-II title, then move on to wrestle with the big guys. Many years we had at least a couple of D-I All-Americans.
And as was pointed out, from time to time, there would be national champions from the lower divisions. I recall a year when I was in high school when Clarion State (D-II) had three D-I national champs. Had the non-D-I teams been allowed to score team points, they would have contended for the national title.
I think it would be great idea for the NCAA to bring this back. With the annual axing of programs at the D-I level we keep seeing, it would be an ideal time to do so.