Multiple reasons in no particular order:
1. Administration decided it wanted to "clean up" the football program and its rogue national image.
2. Poor hiring choices across the athletic department and coaching staffs.
3. The loss of the Orange Bowl and the home field/recruiting advantage it gave Miami.
4. The disparity between the quality of high school football in South Florida and the rest of the country closed.
5. Losing Florida off our permanent schedule hurt us in a profound, immeasurable way.
6. Joining the ACC and playing a stale, largely uninteresting schedule every year.
7. Falling behind in the facilities arms race.
8. The college football landscape changed. Bigger schools with larger financial resources now have a more pronounced advantage than smaller schools with smaller financial resources. Hiring a top-flight coaching staff is out-of-reach for most of college football.
9. No on-campus stadium.
I could go on, but you get the idea...
That's a great description of the Canes. The OP seemed to be focusing on Dolphins and Canes as a combo, but few if any have addressed the Dolphins.
The Dolphins made an awesome hire with Joe Thomas. Consequently the team was loaded before Shula ever arrived. I was a kid but it was obvious at the time. I'm sure it was one of the reasons Shula took the job in the first place. Then along with Shula there were a string of sharp guys like Monte Clark and George Young and Bill Arnsparger and Bobby Beathard and Howard Schnellenberger. I associated the Dolphins as sharper than the next. That's why the move to acquire Paul Warfield was not a surprise. Intentionally surrendering the safety to the Steelers in the 1973 Monday Night game was not a surprise, even if the Monday Night Football crew on ABC didn't see it coming.
That franchise got lazy once Marino arrived. Instead of Shula maintaining everything he believed in and using Marino as a sweetener, Shula succumbed to cupcake football late in the 1984 season. There is a clear dividing line when the rushing attempts plummeted. Then they never came back. There were absurdities like leading the Chargers by considerable margin throughout the 1994 playoff game yet being out rushed 40 attempts to 8. That stuff was being mocked in Las Vegas circles. The Dolphins under Marino were always a laughingstock when I was there. The sharp guys were always looking for spots to oppose the Dolphins.
I assumed that was consensus everywhere. Then when sports message boards popped up on the internet I was beyond stunned when Dolphins boards somehow lauded Marino and praised those years. It is still difficult for me to believe. I considered it insulting football, given the physical resourceful roadmap predecessors of the early '70s. But the AFC in general was insulting cupcake football for a full decade, leading to one refreshing NFC Super Bowl massacre victory after another.
Obviously the new stadium and its site were a disaster. Joe Robbie was broke by ownership standards so he sought cheap land. That stadium was open to view while under construction at Christmas time 1986. I'll never forget it. My dad drove the family there to take a look. You could literally drive up the ramp. It was such a nothing location. I was shocked. The configuration could not have been more bland. We drove away and I felt confident the Dolphins would never win anything of consequence at that location.
I had no idea the Canes would be idiotic enough to follow. But it was preceded by idiotic enough to join the ACC, which owns the devastating combo of non-interesting opponents but ones which own plenty of talented enough and scrappy enough athletes.
On the Rivals board more than a dozen years ago I basically predicted how the ACC switch would pan out.
I don't feel awful about it because I remember when this program was nothing and never expected to be anything. We aren't being cheated now. We were gifted over those 20 years. These days given the format a national title requires three postseason victories and no worse than a 14-1 record.
Lotsa luck. I am not kidding myself. 2001 is going to be 20 years, then 30, then 40...