The presence of chlorine does not make a chemical toxic.

Are you a chemist in the sense that you run a drug store?

Table salt has more chlorine by mass than sucralose. Moreover, in your body, table salt dissociates into a chlorine ion, whereas in sucralose it's covalently bonded into the molecular structure. That's not to say that it is suddenly nonreactive, but being covalently bonded tempers some of it's electron craving, so to speak. By your logic, table salt should be orders of magnitude more dangerous than sucralose (it's not).

Edit to add: Do you know of any mechanism by which sucralose could cross the nuclear membrane? If not, sucralose isn't going to be touching DNA at all. It could touch some form of RNA in the cytoplasm, which isn't necessarily innocent, but it's not going to be touching the DNA. That means it won't cause long-term genetic changes or damage; any damage it caused would be transitory to the working set of RNA and that damage would be gone when that RNA was processed/destroyed.

You are saying that sucralose (or a metabolite thereof) could alkylate DNA - and theoretically proteins too - correct? Like what sulfur mustard gas does?

I did a quick search and couldn't find any papers demonstrating a mechanism of action for that, although I skimmed a few that postulated that a dichlorinated hydrolysis product might be the true carcinogenic agent. Do you know of any studies that demonstrate that the alkylation can happen, either in vitro or (ideally) in vivo? Or maybe some better search terms to use, that could be my issue...

I am truly curious about this, I never knew the chemical structure of sucralose until I read your comment and subsequently looked it up.