For this reason I do the exact opposite on female vocals: cut out the performance and just listen to the inhaling gasps on loop.
I used to cut every breath just because, but I was listening to some stuff like Taylor Swift and realized that they don´t bother me at all. Nowadays I leave them unless it´s something distracting.
I'll leave them on the main vocal track but mostly either if it's in a quiet section or right before something gets blasted out as was previously said
Doubles, harmonies, extra backing tracks I cut them out but as was also said it really depends a lot on the style of song/genre
The problem is that lots of us smash the vocals which brings the breaths out. As with everything, automation often offers the best compromise.