equating respect for language with usage of the letter and vague guilt-tripping of people who don't use it is elitist

Indeed, anyone using ‘q’ is better than others.

Oh wait, could you please check real quick if ‘ё’, a letter of the alphabet taught in school, maps unambiguously to a specific sound?

the modified letter was proposed but never made generally mandatory

Well maybe it was proposed because ‘ё’ denotes a very particular sound? Which, notably, Western languages can never quite approximate with their feeble ‘yo’ attempts, though Nordic languages do have a vaguely similar ‘ø’ or somesuch.

The name Егор doesn't follow it, but моего and сегодня do. Why?

Well, perhaps because the letters are in a different position? Why is /ˈlɔɹəns/ of Arabia not pronounced akin to /ˈsɛsəl/ B. Demille?