At an ORACLE shop I worked at for many years, schemas were used to encapsulate procedures (and packages) that applied to different front-end applications. A different 'API' schema for each application often made sense as the use cases, users, and system requirements were quite different. For example, one 'API' schema was for a development/configuration application only to be used by developers. Another 'API' schema was for accessing the client data via views and procedures (searches). Another 'API' schema encapsulated code that was used for synchronizing development/configuration and client data with an application that had it's own database. Some of these 'API' schemas, under the covers, would still share common procedures and functions with eachother (via other 'COMMON' schemas) where it made sense.
I will say that not having a schema is probably not the end of the world, though it can be very helpful. Really, it is the lack of packages in SQL Server that really creates problems in my mind... but that is a different topic.