Modern Linux distribution pipe the stderr output of applications to journald instead of ~/.xsession-errors. We should consider doing the same, possibly as an option, possibly by default.
This is the commit for GDM that does this:
It is becoming very common that desktop environments or applications log to the journal directly themselves, which means that we already have to ask for output from the journal to get the complete picture.
So this issue is getting more important so we can have all logging in the same place.
For added convenience, we should log the logind session id somewhere, making it easier to filter out the relevant log data.