Several people have suggested that revision control might be an alternative to creating a class of databases. I really have no way to counter such an argument because I cannot fathom what they were thinking in the first place.
The two concepts target completely and utterly different things. I guess that all I can really do is talk about how different they are and hope some people change their stance.
Revision control (e.g.: CVS, Subversion, or Perforce) allows you to track and manage the changes you are making to source code. The point is to (a) provide a place of safekeeping for your documents of design and (b) to allow you to access previous versions of a design. When you update the design of a class, you create a new version of it in source control and do not generally see older versions unless you go looking for them.
The point is to allow you to work on the most recent design in a particular branch while keeping a history of what was done and not betting on a single computer to keep your source code safe. In short: Source control is about managing the relationship between developers and designs.
A class of databases has a totally different functions. Like any other class, it's most interesting relationship is between it and its objects. Yes, a database class must store the steps required to build older versions in it but for a totally different reason that why a version-control system stores older versions of source code.
Whereas a revision control system tracks versions for the benefit of the development process, a class of databases must track revisions for the benefit of the database-construction process.
Storing the incremental deltas required to get from each version to the next and forcing all databases in a class to follow the exact same path of growth enables test-driven, agile database development in two ways. For one thing, it drastically simplifies the database deployment model; every single database of a given type grows exactly the same way. For another, it allows you to properly test the transitions from one version to the next.
The versions of a source file are created because a developer has learned something, changed his mind, or otherwise revised design and they are created to ensure that developers can revisit previous designs. The versions of a database class are created because a revision to design was actually released to production and they are created so that every database in a class is built in the exact same way as every other database in that class.