> $x is pumped into the system by the punters, $y is extracted, $z is returned. The 'house' is the only winner.
This is incorrect, specifically with regard to sports betting. Sports betting and poker are both winnable games. Most people don't win in the long run, but unlike in table games (Blackjack, etc.) there are absolutely winners that are not the house.
To be clear, that doesn't mean they're good or should be allowed. I used to be a poker player and enjoy putting some bets on football now, but I've come around to the general idea that sports betting in particular is a net negative for society. Still, if you're going to make an argument against it, it's always going to be a better argument if it isn't built on a basis that's just factually untrue.