I think you miss the most critical points of EAV data models:

a. "models" in general, not just data models, are abstractions that help humans understand a process or a system. A conceptual or logical data model describes the underlying business as a relational database, derived by a data architect working with the Subject Matter Expert to rapidly build the correct database structures that "model" the business or process.

b. The physical databases implemented from a logical data model will automatically enforce database integrity: both entity integrity and relational (foreign key) integrity.

c. The ANSI - SPARC three-schema architecture, supported by high quality data modeling tools like Embarcadero's ER Strudio and ERWin, does the coupling of conceptual, logical and physical models and keeps them in sync. Tremendous value.

d. The physical database is, or may be, just one of several possible implementations of a logical data model.