Many sportsbooks actually do not run that way. The name "sportsbook" implies that they do, but that is an older style of betting that has fallen out of favor. Modern sports books usually use fixed odds set by an oddsmaker (in modern times, algorithms set by the oddsmaker), but those odds are allowed to float with the probability of the outcome changing. I believe they take supply and demand into account, but you actually are betting against the house. That prevents the kind of trading against the crowd that would be normally viable.
The Hong Kong horse race track was a famous example of market-priced bets where the book was run the way you said and the crowd was exploitable in the way you are suggesting. It was one of the last books to work that way.
The Hong Kong horse race track was a famous example of market-priced bets where the book was run the way you said and the crowd was exploitable in the way you are suggesting. It was one of the last books to work that way.