Is there a reason why the passive and the potential form in Japanese are identical (at least for える/いる verbs)? I mean, does one etymologically derive from the other? Or were they perhaps modelled on a similar original form? If so, how does the え form for other (non-える/いる) verbs fit in?
Etymologically, various usages of れる/られる derived from one base meaning, "without someone's will". In modern Japanese, れる/られる is still sometimes used in this sense (known as 自発【じはつ】 or "spontaneous"). See: Why is the passive form used in this sentence?
故郷【こきょう】が思【おも】い出【だ】される。 I (spontaneously) remember my hometown. (I didn't intentionally try to recall that, but it occurred to me.)
Then the "passive" sense came into use. I think the reason is straightforward; the passive voice is basically used to describe something that happened to you without your will. This also explains why Japanese passive voice often implies that you were negatively affected (aka 迷惑【めいわく】の受【う】け身【み】 or the "suffering passive").
雨【あめ】に降【ふ】られた。 Rain fell (against my will, and I was bothered).
The "potential" sense of れる/られる originally derived from the negation of 自発【じはつ】. Something like "it never (naturally) happens that ～" or "not in the situation where ～" eventually became "cannot". The non-negative potential sense (i.e., "can") followed.
(archaic Japanese) 弓矢【ゆみや】して射【い】られじ。
It never happens that you shoot them with an arrow.
→ You cannot shoot them with an arrow.
≒ (modern Japanese) 弓矢【ゆみや】で射【い】られない。
れる/られる also has an "honorific" meaning. This is also an extension of "not my own will" (i.e., it's the will of "your highness", etc.).