It's a simple theory really...
In Y1, elemental legendary primaries (particularly from raids) were highly sought after and I would consider many of them to have been far superior to exotic primaries simply due to the elemental damage.
Now, in Y2, Bungie has stated several times a move AWAY from these beloved primaries in favor of kinetic damage, but I can't recall an instance where they specifically said why.
I believe this was done for a very simple reason (and kind of a lazy one). It's to make a way for Exotic primaries more sought after in the future. Simply making all, most, or even a few (like currently) Exotic primaries have elemental damage attached would make them so much more desirable. For example, look at the popularity of the Zhalo Supercell currently. Whenever there's arc burn I bet most players who have one bring it. Now, imagine if that gun did Kinetic damage like the rest. Hardly exotic at that point and thoroughly mediocre - I doubt it would see much use.
I think it may have been a test. To see if a very average gun + elemental damage in a kinetic primary world setting would see a spike in popularity. I'm guessing the answer is a resounding "yes".
My theory is that future Exotic primaries as well as some "reworked" or "brought forward" primaries will begin to have elemental damage in the future to make them more attractive while also being able to better balance them for PvP. Future exotics will be average power weapons with an element damage added to them to make them less overpowered in PvP while simultaneously attractive for PvE compared to their legendary counterparts (which would all still have kinetic damage). Not to say ALL exotic primaries will have a damage associated - exotics tooled for PvP use likely won't (I'm looking at you No Land Beyond).
What do you think?
TL;DR - I think Bungie plans to give elemental damage to exotics in the future while leaving legendaries to do kinetic damage.
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I think hardlight should be arc