One of these ratings does not belong

#12 I believe that the essence of correspondence chess is producing games of highest possible quality, and modern high-level official correpondence competitions would not make any sense without computer assistance. Also, a participant of such a competition would not have any chance if (s)he did not use the computer. :-)

But when people play just for fun, the situation is different, and it is really good that the rules you mentioned apply to lichess.org.

RE: #20
I meant that it's also a measure of what I jokingly called "winning mentality". Correspondence chess rating is therefore a more complex measure. By any reasonable definition of "chess skill", ideally, a measure of it should be based on fairness in the game with regards to all components, among them, crucially *time*. Correspondence chess is fair only in a contractual sense. The players acknowledge the uncertainty whether the time spent thinking will be proportionate.

Correspondance chess in schools: The students get to finish their game the following noon hour. No stress of time.
A 90 minute hour glass timer in a correspondance game could help pace the game for the students. That way one game does not last a month.