Why is a glaze applied to the top of a hot cross bun?
I would say that it's not required for any scientific reason. I believe that, traditionally, it's common to put a sweet topping to add an extra hint of sweetness to the buns, which are generally not very sweet themselves. 

It may be in the US that it's more common to make the cross out of the glaze rather than creating a cross in the dough using a paste. When I found recipes from England (along with the one you linked from Australia), they both use the flour paste with a light glaze over the entire bun. This BBC recipe, specifically, uses a glaze made from apricot jam, which sounds very nice.

The American recipes tend to not have an all-over glaze, preferring to simplify the preparation process by making the cross with a white sugar icing after the baking process is completed, though (as seen as an option in this Martha Stewart recipe) you could certainly glaze the entire thing, as if it were a doughnut... though this would leave it without the traditional white "cross" on top.

But, as you can see from the images of the American recipes, provided there's a good eggwash before baking to make the buns golden, they should also get a nice shine, so the glaze shouldn't be necessary for that reason... and without, I'd think it would make them easier to handle, as they're not as sticky all over.