Ironic.
It doesn't, though.
A target-locked effect of finite duration that deals a fixed amount of potency over that time with modifiers snapshotted upon initial cast (call it whatever the heck you like, if "DoT" somehow won't suffice) will not increase your melee uptime unless except insofar as it replaces the time otherwise spent on a melee tool (replacing that with something of greater range and therefore able to continue attacking when you otherwise could not).
A tool like old Requiescat that allows you to continue dealing (nearly) full damage (all but AAs) for 9 GCDs regardless of range is something that can potentially increase melee uptime, but Living Shadow acts independently of the time spent on melee skills while it is active, because it's oGCD.
"Well, Living Shadow is still attacking anyways" is not a reason to feel fine about not attacking, yourself, while Living Shadow is up. Your uptime and that of LS's DoT/summon-without-any-properties-of-a-summon/pet-that's-not-a-pet function independently of each other.
So no, Living Shadow is not a "ranged attack" in even a single way that has ever been useful in XIV in the context in which it exists (PvE). It has every characteristic of a single-target DoT --that simply happens in this case to be oGCD-- and no characteristics or uses beyond that.
On the larger topic:
What kind of interplay with the Living Shadow do we want to see?
Let's throw ideas at the board, simulate them for their effects in-practice, and see what seems lucrative.
Some rough ideas mentioned thus far:
- Living Shadow would instead cause using any GCD while still on the global cooldown to have your Living Shadow perform the attack instead (therefore without incurring the global recast time), with each oGCD granting a temporary charge that allows your Living Shadow to perform it. (Your Living Shadow will automatically teleport to enemies when directed to use melee attacks on enemies out of range, and pressing Living Shadow again while it is active would allow you to switch places with your Living Shadow.) Effectively, a different-feeling Haste buff with some extra bells and whistles. [Synergetic context: Edge/Flood are replaced by a dynamic follow-up version of DA.] -- (Based on my ideas early in the thread.)
- Make it an actual pet, and let it do things that leverage its actually being a pet. About 3 command actions should do, some of which could probably be swapped (temporarily upgraded) actions. -- (Based on Fulminating's ideas, this page.)
- Living Shadow gets empowered by use of certain abilities, perhaps stacking (culminating in a thus-empowered sort of Shadow-Confiteor based on the number Edge or Bloodspiller, etc. casts) or in a sort of "combo" system (to be decided). -- (Based on Lyth's ideas, this page.)
- Doesn't need to be anything too fancy in itself, so long as its (allowances and constraints in) timing forces a significant increase in the kit's total engagement. In that sense, even just a percentile amp could do a fair bit of good for the kit well beyond what LS does now; though that increase wouldn't need to stop with a mere basic damage amp, emphasis should fall equally on the timings of the skill and its impact on (expanding) DRK's fixed CDs' usage (or, options and considerations therein). -- (Based on a frequent/shared idea.)
- Discrete actions, similarly to Salt and Darkness (either on LS itself, or such that LS unlocks these for other skills), or perhaps 4th-step combo skills, etc., such that Living Shadow allows for whole new animations and bonus potencies. -- (Based on Zairava's ideas, previous page, themselves influenced by Lyth's and others', iirc.)