Strange use of Database Schema (Namespace)
I really disagree with your statement that "database schema helps grouping tables, or help identify multiple tables that have the same table name." Actually database schemas were originally created to address security issues and security groupings. Unfortunately, in all of the worksplaces and projects I've been involved with, schema is synonymous with namesspaces (group names). This is just bad design in my opinion. 

You want to create a new schema for every user, but how many users will there be? You don't want 1000 schemas in your database. Schemas are registered in the metadata as unique objects, and there is a limit 2,147,483,640 - they are considered objects and the more objects you have the higher the overhead. The limits are set based on the SQL product you use. The number I gave was for SQL Server