The same reason most people said "why waste an exotic slot on a heavy?". I didn't know better at the time, and by the time I realized it, I was too invested in all three characters to delete one for the scarf.

You ain't man enough to delete your third class on a whim for that scarf? You don't deserve it!

"why waste an exotic slot on a heavy?"

Fools. Unworthy to wield ultimate power.

You could equip the scarf and get 3 light. You still have your scarf right?

Sometimes I lay awake at night wondering why I ever discarded it.

This may be well known, but was unkown to me. If you're wearing an exotic cloak and swap allegiance to another faction, it will disable the cloak. You lose the perks and light from your cloak while it is equipped. I swapped to another cloak and can't equip the exotic one until the weekly reset.

Anyway, if you want to do the no-cloak hunter look, this is one way to do it.