This is attractive in theory but it's a bit difficult to do in practice. Usually the places with the worst comparative odds are also quite aggressive in banning sharp accounts (including any proxy accounts you'd set up as this rival sportsbook). You've got to take the vig into account, as well, which is likely high. So in most cases it's probably not be worth the cost. Especially when there are plenty of other ways to use sharp information to make money.
It's not worth it. Even if they don't ban you outright, the stakes/winnings are very limited for that kind of thing to make sense.
And then there are odds data services like Betradar which provide every subscribing bookmaker with enough near-live data to instantly improve their prices so as to make any arbitrage very hard.
(source: worked at several bookmakers)
As the book who accepts smart money and has non-anonymous customers, you have a more accurate idea of the actual odds than anyone else.