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Exactly! The placement of the comma in English is arbitrary, and where you put it changes the meaning completely.

A translation into English, with correct punctuation consistent with the broader context and yielding the correct meaning does not give anyone the authority to change punctuation to give another interpretation that undercuts the entire theology and teleology. Here the interpretive placement of the comma is not arbitrary.

Your simplistic approach lacks support of both immediate and broader context, and is thus incorrect. In fact, on close inspection, that interpretation does not even make sense. It trivializes the significance of the promise to the repentant, believing, confessing malefactor into a casual comment, of the type "This day I say unto thee, it will rain." rather than "I say unto thee, this day it will rain."

You might check DRB, where a colon for the comma, and substituting "this day" for "to day," reinforces the same sense given by the KJV reading, and either is done by those to whom the Koine is a familiar, intimate, second language.

You might further note that the second person pronoun in "to day thou shalt be with me in paradise" is singular in number, thus excluding the unrepentant malefactor, whose destiny is to be waterless Sheol/Hell, not paradise -- in the very same day.

A study of precision in using the science of hermeneutics will improve your interpretation techniques, as well as the direction you are giving others, will it not?

The placement of punctuation when it does not appear in the Greek is not arbitrary but has to make sense in English.
Here in Luke there is two ways of adding punctuation when translating and both are proper English.

So the translator can look at the context to choose where or even if to place the comma here in Luke.

Jesus’ words were certainly not casual but deeply reassuring to the man asking to be remembered favorably, “When you come into your kingdom”.

“I say to you today (or this day)” is a Hebrew idiom that expresses certainty. You’ll find it used this way in other passages of the Bible. For instance, in Deuteronomy 30:18 we find, “I announce to you today that you shall surely perish. . .” or in Acts 20:26, “I declare to you today that I am innocent of the blood of all men.”

Further, “paradise” is only found in two other places in the New Testament and both times refers to being in God’s presence (2 Cor 12: 2-4, Rev. 2:7). Since Jesus, by his own words, said he would be in the grave for three days, and after resurrection told Mary and others that he had not yet ascended to his Father, it is difficult to accept that on the day of the crucifixion he took the thief to paradise (into God’s presence). The notion that Jesus meant a sort of “holding pen” for the righteous dead until Jesus ascended to heaven is a concept out of Greek mythology.