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Now isn't the provider just as liable to pay the player their winnings as the host platforms?
The provider has no financial relationship with the clients. The provider has a financial relationship with the casino, meaning the provider's client is the casino. The provider is responsible for providing access to gambling and matching these games to the specified parameters (for example, RTP). The provider has nothing to do with any issues of identification, deposits, or withdrawals of gambling funds.
One correction would be that odds providers can profile players and can auto limit sharp players for the sportsbook. Obviously the book can override those limits. They can also warn the sportsbook of possible multi-accounts. Each book is different as some do all the profiling in house. Some even make their own odds.