Most private trackers are using the same pretty dismal PHP bit torrent tracker libraries/servers that work with mysql or sqlite. It would of course be possible to replicate these or do something as simple as cron jobs, rsync, etc., but that's not often the real issue.
The larger issue is the legal aspect. Most of the time a big tracker is taken down, the owners are known to authorities or don't want to risk being known, even by association. As such, continuing the same site, even under different management would put them at risk. If I remember in the case of what.cd and a few others, they put out notices saying they intentionally nuked their databases for this among other reasons.
If for example a big site shuts down and one of the members spins up a new instance, the fear is that the original owners would be liable. It doesn't matter if this holds up or not in court or is even a real thing, merely the threat of it is not worth the trouble to many people. Not many people want to sign up to go to jail or deal with financial threats because of sharing movies or music.
Distributing the database doesn't solve the legal aspect. In fact, distributing the database might be seen as more ammunition to threaten the original site admins as being "enablers." So in theory what you are saying makes sense and would be a good idea, but in the face of reality and human behavior, it is much harder and more than a technical issue.