Editing breaths out of back up vocals and harmonies is a good practice, as it prevents oddities in the vocal performance that may distract the listeners. These can include things like phantom breaths that are under the lead vocal, that can sound very odd and out of place. Another issue would be when all the back ups and harmonies have the breath in the same spot, and you get this very extreme exaggerated breath, that just pops out in an unnatural way.
It's a good practice to just remove the breaths in the background vocals, and let the natural breaths in the lead vocal be present... But, make sure to control those breaths in the lead a little as well.
If you have something you'd like explained about recording, mixing or mastering, feel free to leave it in the comment section below.
Happy mixing, everyone!