Top sports books do that already. Lesser sports books don't have enough liquidity to react in real-time. In fact a simple winning strategy is to check what odds Pinnacle gives and see if any bookie offers better odds (arbitrage betting). It will only work for 2-3 bets before you're rate-limited though.
Yeah this is the entire business model of oddsjam. They basically offer a service that compares all book odds to pinnacle and call it "plus EV betting".