CMB as an ideal black body

Why is the cosmic microwave background such a perfect black body with a Planck-spectrum and why don’t we see the recombination lines of the atomic levels?

maths bonus question: What’s the reason why Christoffel symbols \(\Gamma^{\alpha}_{\mu\nu}\) are required to be symmetric in the lower indices \(\Gamma^{\alpha}_{\mu\nu} = \Gamma^{\alpha}_{\nu\mu}\)?