Some mastering engineers ask for stems because they regularly get such bad mixes that the vocals need to be brought up, or the percussion brought down, etc. But really it should just be sent back to mixing to fix those things. A good mastering engineer knows this.
Some mastering engineers may take stems or tracks for analog summing. Some engineers want a certain analog saturation that they feel can't occur in the digital domain. And some engineers believe that an analog mixing desk simply combines the tracks or stems together in a more pleasing way than the master fader in a DAW is capable of.
If you're mixing your own stuff, I don't see a reason to bounce out tracks to audio. Unless you're running out of processing power, that is. (As others have said.)
But mastering is different. That's as much about getting a fresh set of ears and a fresh set of speakers helping you with your project as it is about making your stuff louder.
Mastering is also about matching levels between multiple songs on an album, setting the amount of silence between tracks, and matching the tonality of tracks to make sure they all sound equally bright and full to each other (and to other popular songs in the genre).
If you have to master your own stuff, add just the two-track audio from each song in your project into one combined new session. Match the volume levels for each, and add plugins to control the dynamics and tonality to match each other. You can add a limiter to the master bus (in your session of finished two-track songs) to bring the overall volume up. But make sure it isn't the kind of limiter that pumps the volume, and don't push it too far or you'll ruin the sonic integrity of your song.
And be sure to audition your tracks on many, many systems, like your car and living room and earbuds and your friend's hi-fi stereo. It's not as good as having an experienced engineer on an accurate system prepping your music for playback on thousands of different systems, but it's a whole lot better than not doing it. Your music needs to sound good on every device, not just your mixing monitors or headphones. And mastering is all about giving your track transferability to your listeners' playback devices.
