something is done
has been done
remaining state
Structure
- Verb[ て ] + ある
Only used with transitive verbs!
[State of an action remains]
It feels to me like, for this grammar point, there should be a parallel with である and the copulas, as it’s exactly the same idea.
Noun + [で] + ある - is (noun)
Verb[ て ] + ある - is (verb (as in the state decurring from that action))
Or am I colossally wrong and there is some other nuance exists? The grammar page, especially the examples, seem to associate てある with the present perfect (and also include a subject that is implicit/unknown in the original sentence), which bothers me a bit.
Are you suggesting to combine the grammar point? If である is a formal written replacement for だ/です、while てある is a transitive verb modifier, I would prefer the separate practice as this is quite a distinction IMO (even though both state of action vs. state of existence behave sort of similar when using ある). I haven’t had the chance to to use/read である all the much either. However, your suggestion helps me remember better so it’s a nice parallel to mention.
Nonono, don’t combine it, that would be bad, especially considering である is far more basic than this grammar point. I simply suggested explaining てある through the parallel with である, emphasizing the fact that, like the copula, てある doesn’t really map to an English form all that well.
である is very common in Japanese dictionaries, which I’ve come to use more and more.
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I’ve often seen that you’re supposed to change を to が when you make てある however several of the sentences still have を. Is this not a hard rule?
Edit: Nevermind, the Maggie link had the answer. However, it may be worthwhile to note on the grammar page that using を is somewhat of an exception for this grammar point.
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Hey 
てある implies that the human did the action, and is limited to transitive verbs (this is what implies the human subject doing the action) only. The subject is often omitted, usually because it is not known or is not important for the speaker.
ている does not have that implication, it simply a statement and the verbs do not have to be transitive (not to mention the verbs are usually intransitive with ている2);.
To sum up:
ドアは開けてある
Doors are open. implies human action.
ドアが開いている
Doors are open. statement of fact, no implications.
I hope it helps,
Cheers 
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Great explanation, thanks!
Maybe the information about it usually being used with intransitive verbs could be added to the summary of ている2?
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Are there any reason or nuance behind the usage of を in situations where preparations are done?
It’s that the beginner-level textbooks don’t acknowledge that deviation makes me believe It’s either solely stylistic choice or too sophisticated to take care of as of right now.
But if I were to make a guess it’s because the subject transfers from the preparations themselves to the thing we’re making preparations for (sorry if that makes little sense).
In the sentence which asks for a remaining state and the hint “have~thought”
次の劇団のセリフをもう___から、早く書きたい。 [考える]
Doesn’t 考えていた kinda have the same meaning as 考えてある in the sense of have~thought?