Like the last two swords, the mail upgrades are completely optional. But in order to stick with the green jerkin, you have to be really good at dodging attacks. The Blue Mail reduces your damage by half; the Red Mail by one fourth. So, for example, when wearing the Red Mail in the final battle, direct contact with Ganon reduces your life by three hearts, and his attacks (trident, fire keese) deplete two hearts.
Doing the math, that would make you loose either 12 or 8 hearts if you're using the Green Jerkin. You only have a 20 heart container maximum--that is, if you found all of the pieces of heart--so doing so would be very difficult. Pretty much, 2-3 strikes, and you're out. As in dead... game over.