I understand what you mean. To avoid the duplication of the voronoi texture you use the checker texture as a mask to blend the rotated and the unrotated coordinates and feed those into the texture:
You need to understand that the texture nodes aren’t outputting images that have transform attributes. They are simply functions that take a vector as input and give you a color/value in return.
In addition: colors, values and vectors are basically arbitrarily interchangeable.
When plugging a white color into Vector rotate the node will read white (RGB: 1.0, 1.0, 1.0) as the vector (1.0, 1.0, 1.0) and then perform a rotation on that vector.
Therefore rotating the output of the texture node afterwords to rotate it doesn’t make much sense.
The manipulations of the transformations of the procedural textures rather have to be done on their input coordinates.
It can take some getting used to, when coming from other systems, since the order of operations sometimes seems reversed, but it is logically consistent and pretty powerful in the way its set up.