Why do the sages care if the condemned continues to deny his guilt to the end?

Question

The mishna in Sanhedrin 6:2 explains how, when the condemned is being led out to be executed, they urge him to confess so he can have a portion in the world to come. This mishna ends:

רַבִּי יְהוּדָה אוֹמֵר, אִם הָיָה יוֹדֵעַ שֶׁהוּא מְזֻמָּם, אוֹמֵר תְּהֵא מִיתָתִי כַּפָּרָה עַל כָּל עֲוֹנוֹתַי חוּץ מֵעָוֹן זֶה. אָמְרוּ לוֹ, אִם כֵּן, יְהוּ כָל אָדָם אוֹמְרִים כָּךְ כְּדֵי לְנַקּוֹת אֶת עַצְמָן:

Rabbi Judah said: “If he knows that he is a victim of false evidence, he can say: may my death be an expiation for all my sins but this.” They [the sages] said to him: “If so, everyone will speak likewise in order to clear himself.”

The sages object because it will look like he's clearing himself, but so what? His confession, in whatever form, is so that God will judge him favorably, and God of course knows whether he speaks truly.

The g'mara's response is unsatisfying; it says that they object so that the condemned cannot bring discredit upon the court and witnesses. But hasn't the condemned been proclaiming his innocence all along? 5:4 says that he can argue for his acquittal during the trial, and 6:1 says that when they lead him out and call for people who can speak in his defense, he himself is allowed to. If the people hearing his confession didn't believe him during the trial, why would they suddenly believe him now? How does somebody saying "I didn't do it" all the way to the end discredit the court that convicted him, given that his saying it before the verdict apparently didn't discredit anyone?

Answer 1

What is the problem with the simple understanding of the Minshna?
The Minshna is saying that we must try to get people to do Teshuva.
Having the ability to say a statement which has the meaning that "I am not guilty I am just a victim"
Which will make people understand this behavior that really this person is not guilty (since this person had the ability to confess and be clean in the eye of G-d (since he is being killed anyway) and he does not, it must be that he is innocent)
in Rabbi Judah's opinion this is OK (since he holds a person in this predicament does not care about people's opinion only G-d's)

But the Sages hold that

“If so, everyone will speak likewise in order to clear himself.”

Meaning that people even in this predicament do care about the opinion of others (even right before getting killed) and will lie just to clean their name in the eyes of the people
This will be a hinderence for people to do Teshuva (to return to G-d Almighty)