Probably a code limitation in that it's easier (backend wise) to "save" a card for your next hand. Playing against the same dealer hand would require saving the state of your previous (first split) deal to prevent dealing from a used hand and overriding a potential shuffle rather than just allowing the game to run as two separate instances with (potentially) a shuffle in between.
Edit: Fundamentally it probably doesn't hurt the odds much since the game runs with at least 4 decks (I've personally seen it throw four of a kind on-suit) but it does limit player information, much like playing solo does.