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We took your query to Boyd Gaming spokesman David Strow. (Boyd owns the Orleans.) He explained that, when loading cash "cassettes" (as they’re termed) into bill dispensers, "you’re trying to go for a denomination that lets go the maximum number of transactions without having to be replenished." (Hundred-dollar bills, twenties, fives, and ones are the high-volume currencies.)
In past years, Boyd properties did load a cassette of $10 bills into each machine, but found – when the cash had to be restocked – tens tended to be still in the drawer. As a result, the company switched over to a policy of loading in an extra cassette of $20 bills instead. That would tend to explain the prevalence of the no-$10s industry practice that you’ve experienced.
Another mystery solved!