If you're using M*v convention (like is typical with OpenGL), the last row stores parameters related to projection transforms. For affine transforms, the last row is always (0, 0, 0, 1). It's fully possible to use only float3x4, but one needs to be careful about the data layout. For genericity, float4x4 is often used, since being the most generic form it allows using the same matrix type for both projection transforms and other transforms.

In MathGeoLib, I have the class float3x4, which I use in my game when I explicitly want to specify an affine transform without projection, or as storage to save a few bits, or when I want to save a few cycles off the computations. Those are rather minor though, and therefore just using the same type float4x4 for all math often trumps the rest.

To further expand, the OpenGL perpective projection matrix is calculated as so:



You need that last row for your projection to work. The 1 in that row copies the z coordinate to use it in the homogeneous divide (there is a point where the view frustum is converted to a 2x2x2 box (each axis going from -1 to +1), and coordinates in this system are called "homogeneous coordinates"). It's a -1 though because of the right hand rule and the way OpenGL's axes work. It needs to be a 4x4 matrix, you see.

Just curious, apart from the perspective projection, is there any other case where you need the bottom row?