You don't need to use homogeneous coordinates to represent a series of linear transformations as a single matrix. That's just basic linear algebra: any series of linear transformations is itself a linear transformation, and any linear transformation can be represented as an equivalent transformation matrix.
But you do need homogenous coordinates if you want to include translations (fixed distance shifts, such as moving the camera) in the set of operations you can represent as linear transformations and thereby gain all the benefits of linear algebra, including the benefit of being able to include them in a series of operations that you can represent with a single transformation matrix.
But you do need homogenous coordinates if you want to include translations (fixed distance shifts, such as moving the camera) in the set of operations you can represent as linear transformations and thereby gain all the benefits of linear algebra, including the benefit of being able to include them in a series of operations that you can represent with a single transformation matrix.