> That's why you always normalize the quaternion first

Again, that won't solve the problem of floating point components not perfectly adding up to one.

Constantly normalizing quats are unnecessary performance hits and worsens your accuracy with no benefit other than being marginally "easier for low-math programmers to reason about", when you could instead just work with non-unit quats homogeneously and divide the final result with the quat square magnitude just once in the entire pipeline, or not at all and instead just pass the square magnitude as your w factor that gets divided on the GPU anyways