These affidavits aren't used to penalize the individual, they are used to protect the casinos from nuisance lawsuits when they escort the individual off the property. Basically, if you sue claiming assault, you are opening yourself up to a criminal charge. It's an effective deterrent.
A casino doesn't ever need to call the cops to deal with you, they have their own private force.
Getting trespassed from an Indian Casino can technically be an international incident; it happens now and then - the sovereignty of tribal nations is a real thing, even if not what you might expect.
Some casinos have public law enforcement, depending on the state. They don't need an affidavit to trespass someone (likely at the summary offense level depending on state), especially since it's all recorded. You shouldn't be able to sue someone while committing a trespass due to the clean hands doctrine, depending on state.