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Godan verbs have the potential form える, while ichidan verbs and 来る use られる for
both the passive and the potential. する also has the passive される, why isn't
that or something like すれる used as its potential, instead of the suppletive
できる?
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etymology conjugations
Why is する's potential form できる?
I can’t answer your question of **why** できる is used as a substitute for the
potential form of する, but let me share what I think is relevant, anyways.

What is now known as the “potential form” started to be used to describe
something’s property, rather than someone’s ability. For example, what would
eventually become 読める meant that a piece of writing was “readable,” or worth
reading, rather than someone was capable of reading something.

Related to this are forms of certain transitive verbs that were used like
intransitive verbs. One example is what would become 切れる, which is still used
as the intransitive version of 切る as in the following example. (In English,
the same verb “to cut” can be used both transitively and intransitively.)

> この包丁はよく切れる。  
>  This kitchen knife cuts well.

知れる is another example. Though “potential” in form, it doesn’t normally
indicate potentiality (可能) but “spontaneity” (自発).
[[1](https://www.nhk.or.jp/bunken/summary/kotoba/term/153.html),
[2](https://japanknowledge.com/articles/blognihongo/entry.html?entryid=380)]
It is now used mostly in certain set phrases in the sense that something is
easily known.

> 彼の気が知れない。  
>  I can’t understand what he is thinking.  
>  (lit. His feelings cannot be known.)

> 彼の能力はたかが知れている。  
>  His skills don’t amount to a hill of beans.  
>  (lit. The upper limit of his skills is known.)

される is similar in that it may indicate “spontaneity” (自発) but not potentiality
(可能).

> 接戦が予想される。  
>  A close contest is expected.

As far as syntax goes, the subjects in these examples are all something, not
someone capable of doing something. I don’t know how and when the potential
form came to be used to describe someone’s ability, but even in that newer
usage, the object of the action is still normally marked with が, as if it is
the subject.

> 漢字が読める。

As for できる, it literally means “to come out.”
[[3](https://www.fleapedia.com/%E4%BA%94%E5%8D%81%E9%9F%B3%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9/%E3%81%A6/%E5%87%BA%E6%9D%A5%E3%82%8B-%E3%81%A7%E3%81%8D%E3%82%8B%E3%81%A8%E3%81%AF-%E6%84%8F%E5%91%B3/)]
If someone is capable of doing something, that thing comes out in a desirable
state when they do it. Though I couldn't find any reference, I suppose the
focus shifted at some point of time from something’s “spontaneous doability”,
which される would have indicated, to how it comes out as a result of doing it.

Note that what comes out is still marked with が as the syntactic subject.

> 接戦が予想できる。  
>  We can predict a close contest.  
>  (lit. A close contest comes out of our prediction. (?))
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answer
I'd like to add some detail to @aguijonazo's post, regarding the development
of the so-called "potential form" or 可能形【かのうけい】 of modern "type I" or
五段【ごだん】活用【かつよう】動詞【どうし】.

### Background

There are a few different theories for how this verb form arose. The most
compelling exploration of this that I've yet read is the 2016 paper
[「可能動詞の成立」](https://www.jstage.jst.go.jp/article/nihongonokenkyu/12/2/12_1/_pdf)
by Japanese linguistic researcher
[三宅【みやけ】俊浩【としひろ】](https://jglobal.jst.go.jp/en/detail?JGLOBAL_ID=201901006631023359).
Miyake starts out with a summary of the main theories:

  * Theory A is the 未然形【みぜんけい】 ("irrealis form", describing something that hasn't happened: also called the "inconclusive" or "imperfect") of the verb stem (ending in _-a_ for _godan_ verbs) + the _-reru_ ending, as previously written about by Yamada in 1936, Yuzawa in 1936, and Fukuda in 1996, among others
  * Theory B is the 連用形【れんようけい】 ("continuative form", also called the " _-masu_ stem") of the verb stem (ending in _-i_ for _godan_ verbs) + auxiliary verb 得る ("possible to", either _uru_ or _eru_ depending on grammatical context), as previously written about by Shibutani in 1993
  * Theory C is the development of intransitive _nidan_ conjugation forms from _yodan_ transitive verbs, as previously written about by 坂梨 (Sakanashi? Sakari?) in 1969 and 2006, Yamada in 2001, Aoki in 1996 and 2010, among others

Theory C is where Miyake lands in his analysis.

### Development

If Miyake's paper is correct, this kind of usage first appears roughly in the
late 1500s, as a kind of shift to the 下【しも】二段【にだん】活用【かつよう】 or "[lower bigrade
conjugation](https://en.wikipedia.org/wiki/Early_Middle_Japanese#Conjugation)"
pattern and to intransitive use, for transitive verbs that were usually
四段【よだん】活用【かつよう】 or "[quadrigrade
conjugation](https://en.wikipedia.org/wiki/Early_Middle_Japanese#Conjugation)".

Looking at the examples provided, this appears to be very similar to the so-
called "ergative" usage pattern in English, where a semantically transitive
verb (a verb that conceptually requires an object to make sense, even if that
object is not stated in the sentence -- things like _" eat"_ or _" read"_) is
used intransitively, and where the subject of the now-intransitive verb is
usually the object of that same verb when used transitively.

Examples of this pattern in English:

  * This stew eats well.  
→ The verb _" eats"_ is semantically transitive (it conceptually requires an
object to make sense). Here, we have the noun _" stew"_ as the subject, when
_" stew"_ would usually be the object of the action of _" eating"_.  
In this construction, we know that it is not the _" stew"_, but instead
someone else that is doing the _" eating"_. Rather, we are describing a
quality of the _" stew"_, talking about **how** the _" stew"_ can **be
eaten**.

  * The paper tears messily.  
→ The verb _" tears"_ is semantically transitive (it conceptually requires an
object to make sense). Here, we have the noun _" paper"_ as the subject, when
_" paper"_ would usually be the object of the action of _" tearing"_.  
In this construction, we know that it is not the _" paper"_, but instead
someone else that is doing the _" tearing"_. Rather, we are describing a
quality of the _" paper"_, talking about **how** the _" paper"_ can **be
torn**.

  * The new car handles like a dream.  
→ The verb _" handles"_ is semantically transitive (it conceptually requires
an object to make sense). Here, we have the noun _" car"_ as the subject, when
_" car"_ would usually be the object of the action of _" handling"_.  
In this construction, we know that it is not the _" car"_, but instead someone
else that is doing the _" handling"_. Rather, we are describing a quality of
the _" car"_, talking about **how** the _" car"_ can **be handled**.

In these examples above, we have the same kind of basic change -- a usually-
transitive verb is used intransitively instead, in order to describe something
about the usually-object noun. This is the same kind of construction happening
in Japanese -- usually-transitive verbs are used intransitively instead, to
describe something about the usually-object nouns.

### The basic mechanism

English syntax (the ordering of the words) clarifies the grammatical roles of
the different words. Japanese syntax uses different mechanisms to clarify this
-- particles, and verb conjugations.

There are many other verbs that distinguish between transitive and
intransitive senses based on conjugation paradigm. In modern Japanese, the two
verb types are more clearly distinct -- things like あく・あける, つく・つける, つむ・つめる,
たつ・たてる. All of these pairs used to have shared dictionary forms (technically
the 終止形【しゅうしけい】 or "terminal form", used to finish a sentence) -- あく, つく, つむ,
and たつ for our examples here. The shifted conjugation pattern from _yodan_
(the earlier version of modern _godan_ , i.e. "type I" verbs) to _nidan_ was
used to mark the shift in valence (transitivity).

In the oldest such verb pairs, the basic _yodan_ form was intransitive (like
つく or たつ), and the shifted _nidan_ form was transitive (like the modern
_ichidan_ forms つける or たてる). This basic mechanism was then later used in
similar fashion to mark the shift in valence for transitive _yodan_ verbs and
their intransitive _nidan_ counterparts.

* * *

### Regarding 出来【でき】る

There was a separate question a couple years ago about the derivation of the
word 出来【でき】る. Please see [my answer post over
there](https://japanese.stackexchange.com/questions/2706/etymology-
of-%E5%87%BA%E6%9D%A5%E3%82%8B-dekiru/18068#18068) for a fuller exploration of
where this word came from.

In specific relation to your own question, the relevant details are:

  * The word itself stretches back to the beginnings of written Japanese in the 700s.
  * The sense _" to be do-able"_ first appears in the late 1600s. This seems to be a reasonable extension of earlier meanings of _" to spontaneously become manifest, to come into being on its own"_.

I am less certain how potential was expressed prior to the appearance of these
two things, the _" to be do-able"_ sense of verb 出来【でき】る and the 可能動詞【かのうどうし】
or "potential verb" forms of regular verbs. Clearly, I should study Classical
and Old Japanese in further depth.
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