This particular case can't be scaled up unless the administration can first persuade hundreds of judges to show a fugitive in their court out the back door. Presumably trying to prevent 'their' accused being arrested in their court -- but the rights and the wrongs of that action aren't decided by the state supreme court, only whether there's a public interest in suspending her while it's pending.
If there were hundreds of utterly spurious federal charges against hundreds of judges (e.g 100 judges charged with having murdered the President, but POTUS is still alive), then their state supreme courts might choose not to apply a principle that "any judge facing federal charges is automatically suspended", since they might not consider it to be in the public interest to defer to federal indictments made in obvious bad faith.
In principle though, I'm sure that federal agents (either at the urging of the administration or otherwise) could attempt to make life difficult for a given state court system, by making false charges against a lot of its judges. Just as they could target any organisation in this way. They would not necessarily need to rely on the state supreme court to suspend the judges in question, since with sufficient false evidence they could persuade a federal court to keep the accused in custody. But, again: as the pattern emerges are federal judges going to believe the evidence put in front of them?
The balancing force is the hope that the federal courts would see that for what it is, and those federal agents would later face charges themselves (for perjury or whatever fits better). The hope is that federal agents and prosecutors, knowing this and also having some basic level of self-respect, will not lightly break the law even if ordered to do so. Whether you share that hope, judges tend to hold quite a high opinion of law enforcement, absent specific evidence against individuals acting badly! So, the balancing force that the judges are looking to is that other judges and law enforcers will not make a mockery of the judicial system in that way.