The potential form of "する" is "できる". However, "～ことができる" can be appended to verbs to create a potential form. Hence, "することができる" can be used as the potential form of "する". While I think there are times this sounds perfectly natural, I wonder if it is grammatically ill-advised, as you are appending the potential form of the verb to the verb to make the potential form of said verb.
The cases where I find it most natural to use "することができる" is when I start off writing or saying something, using the form "～を[NOUN]する" and when turning that into potential form realize it's too late to change the layout of the sentence as I already committed to using "を" (as opposed to "が") and potentially already said "する". Then in hindsight, I feel like the better sentence would have been "[NOUN]ができる".
Is using "することができる" ill-advised? Should it be replaced with other grammatical structures? If so, what are the recommended ways of rephrasing what would otherwise be "することができる"?
Closest related question I could find: ことができる versus V~える form