I would suspect this would require a lot of code edits, as this is something that is hard coded inside XenForo, as it is for every other development project that I am aware of.
I don't think this is something that you can bypass through add-on manipulation either.
I don't know why you would want to do that. It could be a security concern, because if someone were to log in as someone else (staff for example), you would have no way to notice or record it.
Further assuming you edited the core files to achieve this, they would not pass the internal file health checker. Not to add that you would need to do it all over again if you upgraded.
You'll still record the IP address and the staff will still have the power to know who posted what. Which is good, because you don't want people to abuse the system (your site).