It’s a bit stilted and no-one would speak like that (at least without sounding pretentious), but it’s not bad grammar.
Also, shame on the moron that downvoted you for asking a question.
I really don’t see why you would think this.
Sooooo, Carl, on Thursday, said that…
Completely normal thing I would expect to hear.
To be fair, you’ve added commas which makes it a parenthetical phrase. But yeah - people do speak like this in real life; technically, I should have said no-one speaks like this in non-impromptu speech without sounding stilted.
“Carl said on Thursday” is definitely more idiomatic (to my BrE ears, anyway) than “Carl on Thursday said”.