Referential Integrity in schema, cascading the renaming
Referential integrity is one, and is an attribute of the table data, but it is not an attribute of the table's schema. A table's schema shouldn't be changed in a cascading style, because it can break existing working code. A table's column is not used only in foreign keys, triggers, etc. It's used in scripts, maintenance plans, jobs, applications, dlls, even web pages etc. If you change an object's name you can create a mess, that's why it shouldn't be done automatically. This is something you want to control.

This is where refactoring tools can enter the scene. Eg for MS SQL Server there's Visual Studio db projects that can help here, but not by much. There may be tools that aid in refactoring the db objects and fix anything automatically, but they are not part of any standard db package.