We know that a magnetic field in the form
$$\vec B = k \frac{\hat r}{r^2} \tag{1}$$
where $k$ is a constant, violates Gauss' law
$$\vec \nabla \cdot \vec B = 0 \tag{2}$$
Indeed, we have
$$\vec \nabla \cdot \left(\frac{\hat r}{r^2}\right) =4 \pi \delta(\vec r)$$
so that $(2)$ is clearly violated.
Question: does every field $\vec B$ in the form
$$\vec B = \frac 1 {r^2}\left(R(\theta,\phi)\ \hat r +\Theta(\theta,\phi)\ \hat \theta + \Phi(\theta,\phi) \ \hat \phi \right) \tag{3}$$
violate $(2)$ (excluding trivial cases like $R=\Theta=\Phi=0$)?
(I am using the usual notation for spherical coordinates).