Why is Cosmic Microwave Background Radiation thermal? Cosmic Microwave Background (CMB) Radiation is known to be thermal to very good approximation.  This means that when it was created, this radiation has already been thermal.  This is because the outcome of stretching a thermal spectrum (e.g. by metric expansion of space) is a thermal spectrum again.
The origin of the CMB was re-combination of H and He plasma to neutral atoms as it cooled, and that turning from a foggy plasma to a transparent gas "released" the radiation.
What I am confused about is that this radiation was already black-body and has no imprint of spectral lines from neither hydrogen nor helium.  Why that? Or where is my thinko?

Note: There is this answer https://physics.stackexchange.com/a/391849/251841 that just re-states that the radiation was black-body from the start without explanation why / how effects of the electron shells (line spectra) were cancelled out.
Even when there's not enough energy to ionize an atom, there should still be enough energy to make electrons transit from one shell to another?
 A: In the timeline of the Big Bang

The transparency point is a transition from an era in which radiation was strongly coupled to the particles of the expanding universe to an era in which they were essentially free to fill all of space in an equilibrium that is characteristic of a blackbody radiator. The transparency temperature is the temperature at which stable atoms can form, and this leads to a decoupling of the radiation from the particles.

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When the temperature drops below about 3000 K, where a representative energy is kT = 0.26 eV, it is possible for protons to attract electrons and form neutral hydrogen atoms for a reasonable length of time. The high energy photons of electromagnetic radiation interact much less strongly with neutral atoms than they do with the superhot plasma of protons and electrons, so we say that the universe at this temperature became "transparent"

The bound energy of hydrogen, that you would like to see in the radiation curve, is 13eV.At the time of decoupling the average energy for scatters is too small to excite again and de-excite the newly formed hydrogen. Certainly there will be some of that happening , because of the black body distribution there will be also some  higher energy interactions, but the number is not large enough to show up as a signal.
The Cosmic Microwave background radiation is supposed to be   the most precisely measured black body spectrum in nature.
