The Greeks tried to find the perfect beauty in architecture. They searched and studied and finally design sets of rules on how to design beauty. Their architecture is beautiful.
Later the Romans took the classical Greek architecture and used their forms and rules to go further. They built beautiful buildings too and for centuries Europe used the same architectural language to say more and more about constructions. But Romans did not design only temples, theaters, and palaces, they also designed aqueducts and public baths, sewerage, and many other functional buildings.
Someone can say that Greek architecture was purely an art, that no ordinary functions were attached to their constructions, but this would be false.
Even the temples had their function, to be the house of the god, to express the power and the richness of the cities that built them.
I would say that the beauty of the buildings is not an inner art expression, but a form of communication. For this approach, communication is just an act that serves a specific function. This way, artistic expression is another function of the building.
It is not important if this function’s audience is the owner, the public, or both of them, what is important is that it is a function.
So the architectural design is more similar to the product design or the industrial design than of all other art forms as painting, sculpture, or music. The art can be used as a propaganda media and the history is full of examples, from the sculpture of the giant pharaoh to the communist art that was made to develop the socialist citizen.
But the art itself has limited utility for human life. One can argue that we might not need music, dance, or any other art to live. Our human nature on the other hand requires beauty and dance. We can be crippled without art and artistic expressions and communication. It seems that curiosity itself is not enough to go further. It seems that the beauty of the moon made people study physics and astronomy. It seems that even mathematics can bring artistic emotions.
But the architecture is not art. It might seem to be artistic and definitely can and must have artistic value. There is no architecture without a purpose and if one would design constructions without functionality, they would be architectural sculptures, but not architecture.