Great answer. Just to add, this is with red meat where E. Coli is the main concern. That exists in the gut of the animal and that bacteria can travel to the surface of the muscles during the butchering process. Poultry on the other hand is mainly concerned with Salmonella which does live in the muscles of the animal. That's why people aren't ordering rare chicken breast.
"bacteria can travel to the surface of the muscles during the butchering process"
This way undersells what's actually happening: fecal matter from the intestines gets onto your meat. This shouldn't happen with proper practices.
Also, rare chicken breast is apparently pretty unpleasant to eat. Kenji Lopez-Alt did an article where he discussed how you can use sous vide to pasteurize chicken while still keeping it at a low temp, but the result (while perfectly safe to eat) was not enjoyable.