The Cosmic Microwave Background (CMB) radiation is not emitted at the ionization energy of hydrogen, but rather it is a relic radiation from the early Universe that was emitted approximately 380,000 years after the Big Bang. At that time, the Universe cooled down sufficiently for atoms to form, including neutral hydrogen. The CMB represents the afterglow of the hot, dense plasma that filled the early Universe.
The reason the CMB appears as a blackbody spectrum instead of a line spectrum is due to a process called recombination. Prior to recombination, the Universe was filled with a hot plasma of free electrons and protons, which prevented photons from traveling freely without scattering. As the Universe expanded and cooled, the temperature dropped to a point where electrons and protons combined to form neutral hydrogen atoms through recombination. This allowed photons to travel more freely through space without being scattered by charged particles.
The CMB radiation we observe today is the result of this recombination event. It represents the thermal radiation left over from the hot plasma, which has been stretched and cooled as the Universe expanded over billions of years. The photons of the CMB have undergone countless interactions and scattering since their emission, resulting in a process called thermalization. Through thermalization, the initially non-thermal distribution of photon energies evolves into a blackbody spectrum, characterized by a smooth distribution of wavelengths and intensities.
In summary, the CMB appears as a blackbody spectrum rather than a line spectrum because it is the result of a thermalization process that occurred after recombination, where the photons interacted and scattered enough times to reach thermal equilibrium and exhibit a smooth distribution of energies.