We redirect output for all applications in the session to the file xinit.log. This is a direct equivalent to how a local login redirects output to ~/.xsession-errors.
Unfortunately, there is no management of what happens if there is a log data, e.g. for very long-lived sessions, or misbehaving applications. The log cannot be rotated as applications need to reopen the file for that to work, and no applications are prepared to reopen their stdout/stderr.
If the file grows too large, it might fill up the filesystem it is on (which might be /), which in turn likely causes all sorts of issues. If there is no quota set up, then other users, or the entire system, might stop working correctly.
Modern systems have switched away from ~/.xsession-errors to journald, and the size issue might be one reason for that.