Point source of monochromatic photons - self-contradictory in QM?

Suppose we have a point source of photons located somewhere in space.

So when the photons are released their location is well known, $\Delta x \approx 0, \Delta y \approx 0, \Delta z \approx 0$

Heisenberg's uncertainty principle tells us: $\Delta p_x \Delta x \ge \dfrac{\hbar}{2}$, and same with y and z axes.

This tells me that $p_x,p_y,p_z$ can take on any values (since the uncertainties in position is 0).

So the debroglie relation $\lambda = \dfrac{h}{\sqrt{p_x^2+p_y^2+p_z^2}}$ leads to an infinite spectrum of wavelengths.

Is my analysis correct or wrong? Can we have a monochromatic point source of photons?