It has never been standard practice to store the database schema and its history, notes, and documentation in the database, although data dictionaries come close. There are database catalogs that can carry a subset of that information, but a more traditional "90s" approach is to use a data modeling tool.
If you want detailed change history it is hard to avoid using DDL files with source code control, although notes go a long way. Most databases are not good at change history - not even good at representing it, unfortunately.
It is also quite easy to do a mediocre job of anything, and I would be careful of counting anything as the "bad old way" with out a careful evaluation of the pros and cons of the "new good way" as well. A casual observer might wonder why so many modern web apps have response times that are ten to twenty times longer than they were two decades ago, for example. Perhaps - on occasion - the new good way isn't so good.
Sounds like 90s DB admins making a case for the bad old way of doing things.