I'll omit personal references and judgments and stick to dry logic.
It equates to:
Parentified child = E1 fixation
In logical terms:
Parentified child <=> E1 fixation
i.e. they're both necessary and sufficient condition one for the other. One strictly implies the other, both ways.
In order to disprove it, I just can use demonstratio ad absurdum.
First implication
Parentified child <= E1 fixation
It equates to
NOT Parentified child => NOT E1 fixation
It's easy to disprove: one just has to find counterexamples, and there are plenty. I'm sure we all know
NOT Parentified child
who indeed have
E1 fixation.
A random list from the web:
Even if we don't agree on all of them, were they all parentified? A cursory look at some biographies points at that not being the case.
Second implication
Parentified child => E1 fixation
It equates to
NOT Parentified child <= NOT E1 fixation
It's also easy to disprove.
one just has to find counterexamples, and there are plenty. I'm sure we all know
NOT E1 fixation
who indeed are
Parentified child.
It's harder to come up with a list here, but suffice it to say that I know my ESFJ E2 mother-in-law.
A fictional example, as I already mentioned:
en.wikipedia.org
The main character (played by Michael Douglas) is an almost unanimous E3 on PDB
but still has was parentified, he is told so at one point in the movie (he "played dad" to look after his younger brother after their father committed suicide).
TL;DR:
Some Parentified Children are E1
Some E1 were Parentified Children.
But there's plenty of PC who are not E1, and also plenty of E1 who were not PC.
______
As an extra:
I've
bolded traits in your PC definition that do not fit with the stereotypical E1 profile, as we've already discussed here. You argue E1=Ni. I - and others - disagree.
Also, low self esteem is NOT a strait of E1, it's in the 4-5 territory; sometimes in 9 and 6. (stereotypically, I mean).
Equating low self esteem with E1 is plainly wrong, IMHO.
And gifted is not related to type. You have to specify which gifts, at the very least.
Multi-talented, for example, is E7.
Analytical is E5.
Not only, mind you.
The error is the same: you are taking anecdotal evidence and infer general rules from it. It's never that simple. Sorry.
I'm sure you know (are) the case for which they all imply one another, but it's not NECESSARILY that way.