Whats the purpose of synthing guns?

[Nestahima]

I mean, we synth melee weapons to add an element, but what is the purpose of synthing guns or even wands/rods for that matter? Their PAs give them they're elements...

[Flamingo99]

You can synth stronger weapons that you cannot buy at the weapon shops.

[Randomness]

And you can synth them for less than the cost at the shop, if you have the stuff already.

[Nagidar]

I'm actually curious if you can synth Exceptional Results like you could in FFXI, all the good stuff was HQ'd and would cost an arm and a leg.