Breather holes aren't actually for air to go in, the fact that some pens don't have them are proof that they aren't necessary. The amount of ink that comes out is so tiny, you only need a little bit of air to go in from under the nib to prevent drawing a vacuum.
The are actually just there because if you saw a piece of metal it will form cracks and fractures. The hole at the end makes sure the slit terminates there. Nowadays nobody uses saws on metals anymore, so it's really just a remnant of the old design.