Rationale
The rationale is the casino makes the rules, and whatever they say is what ya has ta do. Doesn't have to make sense. Usually doesn't.
Actually, what they're disallowing is not a side bet; it's called back betting. I think most casinos in Europe allow it; most casinos in the U.S. don't. Many U.S. casinos require a player to actually sit at the table. Your guess is (almost) as good as mine...
A complication can arise if the seated player decides to split or double down and the back bettor doesn't have the extra money. Maybe that makes it too complicated for U.S. dealers. Europeans are much more sophisticated.
ETF