I think I'll preface this response by saying I feel you're being particularly argumentative about my posts and comment that I feel that no matter how I respond, you'll find a different detail to nitpick. But here I go to attempt to respond.
I will also preface this particular response to indicate that I have enough knowledge of the DPS and tank classes to gauge what buffs to give as an AST when cards are drawn but not the intimate knowledge and comparisons some players have in their "career choice".
I'll start with me redefining what I mean by sustain after giving the day to think about. In my opinion and thoughts, sustained DPS means DPS that's consistent and doesn't fluctuate too much. SCH, MNK, and SMN would all fall into this category as their kits emphasize this. They don't spike as often as the other jobs but can maintain good and consistent output. NIN can sorta fall into this category too with more readily available spikes via Ninjutsus.
Now, if you were to look at the potential output of the jobs, MNK by design is able to output a higher DPS level than SMN as per S-E's SSS DPS checks. If I were to answer your query above, I would say just this, MNK has higher potential DPS out of the jobs who's kit embody a sustained and consistent damage. Which I know doesn't answer your question but at the same time, to put bluntly, your question makes no sense to me either.
In terms of the context to the comment I made on the 2nd page regarding "highest sustained DPS", you can combine my thoughts about the sustained DPS I mentioned above with the fact SCHs don't consume MP any where as readily as their AST or WHM counterparts. This is because SCH's best healing abilities are either free (fairy) or tied to a resource that is renewed every minute (Aetherflow). Thus, over the course of a long fight, WHM and AST will have far less resources to consume for their DPS compared to SCH.
If resources were of no issue, then yes I would say WHM and AST DPS > SCH DPS. But WHM and AST cannot maintain that level of DPS in most high-tier scenarios without dramatically hampering their healing duties. Therefore I stand by my comment that SCH has the highest sustained DPS of the three healers.
So, what would your definition of "sustain" be? Because I certainly don't understand your context of "sustain" in the way you wrote it in your comment.
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Now, about the second half of your post, I will have to disagree with a lot of comments made here and I'll just do it one piece at a time.
I agree with most of this comment (more about my disagreements later).
If you're taking it from a literal game mechanic sense, this is true. A WHM is either healing or DPSing.
However, consider it from a different context.
What allows the SCH flexibility is the fact they have a Fairy that assists in their healing duty. You can basically say the Fairy is a targetable HoT (it casts every three seconds and has a similar potency level to most HoTs in the game). While a WHM literally has to spend their GCDs either healing or DPSing, it doesn't mean they aren't healing while they DPS or they aren't DPSing while they heal.
Regen provides healing over time similar to the Fairy at the cost of one GCD. The WHM can be DPSing while Regen is ticking, allowing it to perform both duties at once. In fact, Regen + Asylum (also on GCD) provides more healing / tick than SCH fairy will.
Likewise, similar to SCHs, WHM can provide DPS while healing in the form of their three DoTs. Accuracy issues aside, this isn't much different than how SCHs would place DoTs on their target then shift back to healing while their DoTs do their work.
SCHs may have more advantages in the multi-task department due to the GCD-free Fairy, but conceptually WHM and SCH would use similar tactics to optimize their HPS and DPS output.
See comment about Regen (and Asylum / Medica II if desired) above regarding this. WHM loses a GCD, yes, but it's not a harsh impact to their overall play.
WHM has the only heal in the game that actually heals while in Cleric Stance - Benediction. SCH gets Sacred Soil, Eye for an Eye, Supervirus, and Stoneskin (if CC'd). WHM gets Stoneskin, Benediction, Eye for an Eye (if CC'd), and Virus (if CC'd).
All of those abilities outside of Benediction are mitigation tools and not actual healing tools. If you were to argue healing in CS, WHM wins hands down in the fact they have Benediction.
I'm actually not sure what this comment is trying to say aside from the fact "we can do stuff that helps our healing role while in CS that aren't penalized" but those abilities tend to be minimal impact. If you virus a tank / raid buster, you're still going to need to drop CS to heal afterwards anyway.
WHM also gets the same "DoT ticking" benefit as SCH does. WHM also gets Tetragrammaton and Assize though, yes, you can make a case that the cooldowns on these abilities do hamper their desirability.
It's funny because I would argue Essential Dignity being the best single target insta-heal in the game due to 40s CD and having a scaling potency that can exceed Lustrate / Tetragrammaton.
Will not argue Indomitability is the best AoE heal in the game though. But it certainly doesn't mean WHM doesn't have their own equals either.
So... when did I ever mention that SCH is amazing in the off-heal slot only because of their DPS? If you believe I implied that then you're taking my comment regarding sustained DPS well out of context.
Yes, I would agree that SCH has the most healing flexibility thanks to their kit and their options. It is how the kit was designed after all.