Why blow Frank's cover in Ocean's Eleven (2001)?

To make it authentic, real scene

Frank invented the identity Ramon , because he needed a job. At that time, Danny Ocean was at jail and the group was disbanded. Everyone has to work to earn their own living.

While Linus reveals Frank's true identity, later gets him fired (It was Frank's part for the heist and that was enough from him to the plan.), that was not just for some codes but for steal the vault access codes/combination written on a piece of paper in Benedict's jacket. Linus and Frank stage a faux confrontation in Benedict's presence. Making a good distraction for Linus to steal the code.

To make this scene as real, they needed to express something real. You said They obviously didn't expect Benedict to check on Linus's credentials But there were no such indication in the movie for this.

See it like this, Terry Benedict is a character that works right on time, knows every little thing in his casinos, have a complete control on himself all the time, So he will check for Linus' accusations. It was a fact that crew used to make the scene authentic in Terry Benedict's mind, later when he checks for that, There will be actual Frank Cotton and he is every bit of the man that Linus described. So his story checks out and Benedict has no doubt about the scene with Frank, Linus and himself. Danny and the crew used real details to made the fake argument/scene authentic and to prove that it was authentic in the Benedict's mind. If he gets suspicious about that incident, then he starts digging and crew will be caught.

The goal was to obtain the piece of paper with the day's codes carried on Benedict.

Benedict, surrounded by guards, and only rarely, and randomly, stopping as he walks through the casino, wasn't approachable, and surely his guards would have noticed a stranger bumping into Benedict, and the pick. Getting close enough to assure a clean pick was a problem.

This part of the plan was therefore elaborate. They knew that Benedict would personally deal with the Nevada Gaming commission if threatened with closure of the premises, so any time a gaming official requested his presence he would make himself available.

They also knew that any simple play for Benedict's attention wouldn't give the pickpocket enough time, physical contact without suspicion, and opportunity to make the pick.

By creating a situation where the dealer would be upset, claim racism, and be physically imposing, and creating a gaming official that was a meek office worker, they could sell the illusion to Benedict that everything was as it seemed.

They needed to further sell the illusion by having real identities. They didn't choose Frank randomly, part of his required qualities is that he showed up in the databases as a nefarious character. Creating a squeaky clean character with no bad hits in the database is easy, but creating a suspicious character with a rap sheet is harder.

Because they needed that close contact with the highly guarded personality of Benedict, they needed and equally important confrontation with a highly suspect character so assure Benedict all is as claimed, and to avoid looking further into the issue.

For instance, if Benedict had any suspicion that Frank wasn't the bad person he was made out to be, he would have started looking into the gaming commission's employment of Linus.

By using a character easily found within the real gaming commission's database, Benedict doesn't need to investigate Linus.