Following on from Q: Why is accusative pronoun "te" used in this construction?, in this quote from Cicero:
"nihil necesse est mihi de me ipso dicere, quamquam est id quidem senile aetatique nostrae conceditur." (de Senectute 30),
it is clear that Cicero is talking about himself:
"I need say nothing of myself in this connexion, though to do so is an old-man's privilege and permitted to one of my age.".
Therefore, why deploy the intensifier, ipso, the ablative of ipse = "self"?
A couple of miscellaneous points, some iterated from my comments:
You used more words to ask your question than strictly logically necessary. Why did you do that? Cicero doesn't use the bare minimum to convey his message, and neither do you. No one does.
Try not to treat language as a logic puzzle to be solved but as a tool to be used. You seem to start from a premise that expression should be minimal, but that is rarely what languages use is optimised for. Try to let go of that premise.
There was a choice to be made in constructing that sentence, and Cicero might not have meant anything by the choice he made. This instance of word choice sounds so mundane to me that it'd move on.
If there's context that makes the question more meaningful, that changes the matter. I don't see such context here.
Be careful with the symbol "=", both in writing and in thinking. It is not true that ipse = "self". That word can also end up being translated as "very", "exactly", "right", or not at all. Equating two words is easily misleading. Latin and English pronouns work differently.
The translation of your Cicero passage could well be exactly the same with or without the ipso. Translation is about understanding the meaning in Latin and expressing it in English, not about mapping words to words.
If you want to express a correspondence between two words, you could use the symbol "≈" instead, produced e.g. by typing ≈.
Perhaps the word ipso underlines reflexivity. Saying me ipso instead of me reminds the audience that the same guy is both the subject and the object. Redundancy like that is very common and very useful.
Perhaps the inclusion of the pronoun is idiomatic. At least to me it sounds more natural with it than without.
If you scan the text for ipse, ipso, ipsa, you see, that Ciceros Cato regularly uses a indication with an emphazising ipse. This is a regular rhetoric element.
