No. Sustained damage doesn't stop being sustained just because everything is dead. The Reaver does the same continuous steady DPS against a commander (at higher risk) as it does against a random mook. Burst DPS is on-demand damage on a cooldown that is much higher than your normal dps.
Basically, if you record and graph your DPS every second where you're dealing damage, sustained DPS will be comparitively flat, and burst DPS will have significant player controlled spikes.
Not having a target is not the same thing as doing zero dps.
"Sustain" means to maintain. If everything is dead, there is no more damage left for you to maintain. Your damage is no longer being sustained. This is by definition.
You seem to have two different definitions of what Burst means. The latter, which is generally how the term is understood, defines Burst based solely on how the Damage vs. Time graph would look like. For a Reaver, it would look exactly as you describe, with spikes where you're Raging away, and precisely 0 damage when running. Your first definition of "on-demand damage on a cooldown" is one type of mechanism that results in burst, or spike, damage. In this case, your ability to continue dishing out damage is bottlenecked by the cooldown. But it is by no means the only way in which Burst manifests itself. In the Reaver's case, your ability to continue dishing out damage is bottlenecked by the physical distance between one set of mobs and the next, as well as the time spent staying alive throughout all of this.
That is why Reaver is superb burst DPS, but not "floor-wiping" sustained DPS.
Not having a target is not the same thing as doing zero dps.
In fact, it quite literally is. I don't see how you can argue otherwise. To reiterate one last time, every moment you are NOT HITTING SOMETHING you are dealing zero damage, and thus your overall DPS is dropping. That's just math. If it takes me two seconds to run from one mob to the next, I have just dealt 0 damage over 2 seconds. In other words, my DPS for those 2 seconds was exactly 0. This reduces my overall DPS. Furthermore, Reaver's superb burst can quickly destroy that archer you rush, but the maximum damage you actually deal can only be equal to the max health of the mobs you kill. This is the point I was making about overkill damage, which you also did not address. You need to divide all the damage you deal over the total time it took for you to deal that damage, including the time it takes for you to run in, starting from where the AW would have begun attacking.
In a lobby I would consider near ideal for a Reaver pick, where there is a Keeper, a Legionnaire and perhaps a Hunter there is absolutely no way the AW is a superior choice for DPS. Conversely I would not pick a Reaver over an AW in a lobby with a Necro, a Katari and an Archer, but the AW is still not a DPS powerhouse choice (AW DPS IS NOT HIGH).
The question has never been whether or not the AW is a "superior choice for DPS". I have never made this claim. I have only been trying to counter the original claim that "Reaver DPS wipes the floor with AW DPS".
A Reaver doesn't actually need everything grouped together to kill everything fast, it's just that it will kill everything in ~2-2.5 seconds if they are grouped up.
Now, we're getting to the core of the issue. I absolutely agree it will kill everything quickly if they are grouped up, which I've also repeated this several times. The problem is when they are not grouped together, which is the more general and common case. Without a reliable Barrier (another variable, especially in PuGs), and with no Guard generation, a Reaver has to somewhat tiptoe around the battlefield so you don't catch stray arrows to the knee. Whatever tools she has at her disposal either cost a slot or cost precious time. Time spent Not. Dealing. Damage.
You need to accept that in the imaginary scenario I presented, with the Reaver there, everything is dead within 6-7 seconds of the AW casting PotA whether the AW does damage or not. Without the Reaver there most or all of them are still alive even with the AW attacking them and it will probably be more like 15 seconds from the casting of PotA until they are all dead.
I don't "need to accept" anything, certainly not the scenario you presented that assumes the Reaver has an AW teammate who graciously casts PotA for her convenience. In fact, I absolutely reject this premise, but I already voiced this sentiment in my last post.
All of these statements are true, however the damage I was listing was highest possible (non-crit) to a single target for each ability, collateral targets will take the same, or, more probably, less damage.
Maximum CL damage is one target getting hit three times = 750% weapon damage, which is the 1148 average I listed based on the 88 average damage of the staff I listed, with the +45% attack and the additional +20% bonus from the staff of the Dynamo. CL is almost always not going to do that much damage to any single target.
The Stonefist damage I listed was based on the same staff at 500% and the assumption that you will combo it, and that the combo bonus is another 500% damage (this was an incredibly generous assumption). Stonefist is basically guaranteed to not do as much damage as I listed.
We're discussing actual damage dealt, so it makes no sense to only consider one target. No one said anything about comparing how much they can spike on one unfortunate mob. If there are multiple targets (and there usually are), however un-clumped they are, CL will deal its full damage, minus a little bit of overkill, which isn't much. The same cannot be said of the Reaver. On most kills, especially squishies, there is a significant amount of overkill damage, which does not contribute anything to her DPS. The Reaver's output is therefore more sustained on target with a lot of health, but in the game, you deal with a smattering of squishy targets with some tankies sprinkled in.
The Stonefist combo damage isn't necessary, since getting Stonefist to hit multiple targets is a very simple task; the AoE is quite decent.
Gathering storm is a quirky one, in practice if you attack continuously it will drop an 8 second cooldown to about 5 to 5.5 seconds thanks to animation. Expecting Gathering Storm to have a large impact on your cooldowns in a build that includes Fadecloak for damage is... curious.
Dropping an 8s cd to even 6s is very significant. Let's say cast time is 2s for Stonefist + CL? That means your rotation that was 10s long is now 8s long. If you dealt X Damage over these 10s, now you're dealing X Damage over 8s. Your DPS went from X/10 to X/8: that's a 25% increase. In reality, you're losing a couple of autoattacks in there, so the gain is probably more like 15-20%, but I would certainly claim that it's a "large impact".
All else aside, you haven't at all explained how you deal with things that block or otherwise stagger/stun you. Not only are you no longer dealing appreciable damage, you're a sitting duck for anything trying to kill you. Any trick you try (Combat Rolling, LoSing, War Horning, etc.) further reduce your damage output as you spend time dodging about.
For the AW, you don't have issues with blocking, and anything that comes directly at you, you can deal with using Fade Cloak. This is actually my preferred usage of the skill, saving it for things that rush at me or would otherwise interrupt my output. The invulnerability and subsequent massive AoE damage + knockdown is invaluable.