I'm pretty sure the Russos actually said in an interview that he put himself in the lottery to get dusted.

Which makes me think of how fucking badass an ending it would have been for him to do the snap, play the montage of everyone going, and then for him to start fading in Thor's arms, a confident and content knowing look of "I win" on his face as he fades away. And then the heroes are left alone with the pieces.

That seems kind of a bad idea though, considering it'd free up anyone to just use the gauntlet to fix everything. Even if the candidates who can actually use it seem non-existent. (Is there anyone even qualified in the MCU at the moment?)

Makes sense he'd leave himself out, to safeguard the stones. Especially since he's ready to live in complete solitude and not take up any universal resources himself.