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I am not sure if an ability that is just a set of a relatively small amount of already existing abilities has that much use, but ok.
This is a relatively complicated issue when compared to usually making ability pages, because our usual ability pages don't contain this kind of reasoning. Fire Manipulation is listed if you have any kind of control over fire (for example creating fire), but you can not declare someone an abstract existence if he only has one ability which an abstract existence usually has (not every non-corporeal entity can be listed as Abstract existence). In other words as the article currently mentions, it describes a state of being and reasons abilities that a being in that state has, instead of describing an ability like usual pages.
If we do it this way we have to be very specific with the definition of the state of being and have to formulate it in the way that the abilities we want to reason from it are a necessary result. Since fiction is very non standardized and follows many different views/laws this is extremely difficult without requiring the abilities we want to shown to exist to be part of the definition in the first place.
So for short the problem is that not all dragons breath fire, not all ghosts are intangible and not all plants are weak to fire. Similarly not everything called an embodiment of some concept or theme is an abstract entity.
1. Practical example:
Luna Child is the fairy that is the embodiment of the aspect of nature that is the moon. She has basically none of the properties we want though. She can neither manipulate the moon nor its concept, she is entirely physical whenever existing (though her true nature isn't to be fair) and she certainly isn't aware of anything going on upon the moon. She also doesn't regenerate from the concept of the moon, but just from its physical existence.
2. Corollary: We can easily enough construct the same problem as in 1 with something like space instead of the moon.
At this point I might also remind that there is a difference between something like space and the concept of space, even if both are intangible. Space is he practical set of points we life and act in. The concept of space is in a sense just the idea or possibility that there might be some set of points with such a things as distance defined on them. In other words the concept of space is an abstraction, and the actual space is just one possible instance that fulfills this abstract properties. So for our purpose "space" is closer to "Moon" than to "Concept of Space" in nature.
3. Practical example: Relying on what TheMightyRegulator told me I will do a practical example here (if this shouldn't apply or I misinterpret it view this as theoretical example instead). To quote from a thread I talked with him: "It was noted that if Giratinaina ceased to exist, so would its world of antimatter". Giratina is the embodiment of antimatter in Pokemon (not sure if its the concept of antimatter, but lets assume that for this example). If this relation holds true it doesn't fulfill the properties we want though. Because instead of being an entity which physical form has conceptual inheritance from what it embodies (aka regenerates from its concept) what it embodies is destroyed if it dies physically. Due to that the hard to kill aspect, which is probably the most important property we wish from conceptual entities, is not fulfilled.
No matter whether this practical case is as I explained it or not, we see that playing an embodiment of a concept like this is possible and not implausible. Hence we can not disregard that in the definition and have to take care to weed out those cases.
4. Remark: The possibility that a character has conceptual inheritance, but lacks the omnipresence that is currently mentioned as necessary use, is also imaginable.
5. Slightly off-topic remark: Let me also say that if one works with statements regarding concepts and embodiment one has to be careful, as this can often be rhetorical formulations not presenting what actually is the case. (For example "ignoring the concept of xy" is often a hyperbole)
So all in all the current definition of abstract entity is too imprecise to reason the abilities we want to give out for fulfilling it, in my opinion.
The task that would have to be done to resolve it is one of a nature typical to mathematics. Essentially we want to define the term "abstract entity" in such a way (which way is technically not important) that we can without doubt reason from that definition that such an entity has the abilities that we want. That definition is then the criteria a character has to proof to fulfill to have this nature and get having all this abilities acknowledged.
How could that be done? My intuitive understanding of what an abstract/conceptual entity is: "An entity which true form is that of a disembodied consciousness and which has conceptual inheritance (the ability to regenerate from) one or multiple concepts".
So as you can see my intuitive definition clearly contains which are the minimum abilities I expect any a conceptual entity to have, but due to that makes it unsuited for an reasoning from the nature of an abstract being to its abilities: In order to show that someone is an abstract you would have to show that it has the abilities already, which it gets due to being an abstract. So in the end you could only reason from its nature what you already know.
If we want to skip properly defining what an "abstract existence" is we might as well just rewrite the page to be the page for "The ability to [which abilities we want abstract entities to have]", though. That way one actually has directly argue those abilities for the characters one wants to list the ability for though (something I have no problem with, but what might goes against the intention of this discussion?)
Note:
It's almost 6 o'clock here and I just wanted to get something of my work list before going to sleep, so this might be an crappy (and much too extensive) formulation (it was restructured, re-purposed and reformulated multiple times), but I hope I could make the problem, that I see, clear.
Edit: seeing how long that actually got if it is too hard to read I can try writing a better summarized thought gathering, with less irrelevant information tomorrow.
