... It seems to me that everything I would do while mastering is the exact same stuff I could just put in the output chain of the mix ..
For the most part true. Except for-
A second person hearing it objectively
In a second and quite possibly higher quality environment
With somewhere between possibly-to-very-likely more skill specifically tuned to the tasks
You can do it yourself. I have at times. But it can be IMHO a large extra load.
Take on for example an album project for a band. You've recorded it. Did all the overdubs. Put your best out there, and then again in mixing it at which point you're bouncing between micro and macro modes, i.e.
neck deep one song at a time typically.
Now mastering is assembling the songs for the whole. Correcting for all the mix differences
that will be there so they sound cohesive in every aspect -tone, dynamics, levels, assembled a finished set of files –and quality checked...
My experience (minor compared to some) is that when I've finished mixing an album project and slide into mastering mode a few interesting things come up.
Not the least of which is the question 'If I didn't hear these issues at mix why/how the hell would I expect to now? Still me, same room, same speakers..
Part of the answer is you need to hear it differently, and your focus IMO has to change;
You have to make some distance from the micro mode you've been in. And once in that mode, I for one a) get more critical and b) start hearing things that make me want to call up the mixer—

and say hey, why don't you fix all this... stuff you missed?
Self mastering for me has ended up being quite a lot back and forth between
mix-fixes and pulling the whole together.