Is it true that you would not really ever add する to a するverb and then nominalize it with a particle?

Like you wouldn't really ever say something like 野球をすることができます。 Rather, you'd just say 野球ができます。

Right?

To say "I know how to play baseball.", native speakers would almost never say 野球をすることができます.

野球をすることができます, when correctly used, has two meanings:
1. Playing baseball is permitted in a certain place.
2. A baseball player has recovered from a serious injury and says "I can play baseball again."

野球ができます has one additional meaning, which is "I know how to play basebal."

Why not 野球をできる? I mean, できる is already the potential form of する. Wouldn't be like saying "I can do, do laundry" (stupid example, but couldn't come up with one better to try to explain what I wanted to say sorry).

Because potential forms should take が.
I can't tell you exactly why it has to take が if that is what you want to know.
All I know is that you express potential with が.

Edit:
I hope I didn't mis-understand you; When I wrote the above, I was under the impression you wanted to just know if をできる was correct.

But now I have re-read it, I think you want an explanation of the linguistics (If that is the right term to use)

It was more a request about the する and できる used together, seems more a repetition.
As per をできる I was taught that potential form takes を、が、は with slightly difference in meaning (or nuance). But I might remember wrong.

Because you're supposed to use が with potential verbs technically. For example, (a weird and simplistic sentence)　ピザが食べられる is the textbook correct form, not ピザを食べられる. Using を there, IIRC, is "wrong" but people still do it, and I think, like using を with たい form, it emphasizes the object of the sentence.

This is how it was explained to me:

*A direct object in a sentence using potential verb form, can be followed by either "ga" or "o" or "wa"
However, each brings its own different nuance to the meaning.Thus:

A,(watashi wa) nihongo ga hanase-masu.(I can speak Japanese/ The language I can speak is Japanese.)
=> This _expression puts stress on "nihongo" which the subject(watashi) can speak.
* Question: "anata wa nani-go ga hanasemasuka ( What language can you speak?)
Answer: "watashi wa nihongo ga hanasemasu" ( I can speak Japanese language)

B,(watashi wa) nihongo o hanase-masu. (I can speak Japanese )
=> This _expression emphasizes the subject's ability to be able to speak Japanese.
* Question: "anata wa nihongo ga hanasemaska"( Can you speak Japanese?)
Answer: "hai, watashi wa nihongo o hanasemasu"( Yes, I can )

C,(watashi wa) nihongo wa hanasemasu ( I can speak Japanese.)
=> This _expression implies the subject (watashi) can't speak languages but Japanese.
(watsshi wa) nihongo wa hanasemasen ( I can't speak Japanese.)
=> This _expression implies the subject can't speak Japanese ,but other language.