First I should clarify that I don't ask a question like "How do change a Stack Exchange login email?" and there are already such few (duplicated) questions.
I ask the following question to better understand how the Stack Exchange network is structured and if any major change is planned, as I believe it will be helpful for others and for myself:
Why does changing a login email done through Stack Overflow instead through Stack Exchange?
Another question I have that I think both clarifies the need of the first question and derives from it (but maybe best to be asked in a separate session) is:
Why should users change their emails in two places:
Instead in just one?
I humbly assume changing login email through Stack Exchange and in one place instead of two, would reduce system complexity and be more convenient and accessible for users.
Update per answer by animuson
I didn't know setting emails could be done from any site in the network besides StackOverflow and excluding Meta StackExchange; I was used to do so from StackOverflow and assumed it is possible only there as a legacy.