Some jurisdictions don’t allow a guilty plea to a capital crime. Even if it is allowed, the court would likely be very reluctant to accept it.
Well, I know they do allow them here. An intent to seek Death Penalty must be filed here before a defendant makes his plea. In a recent case here, Levi King was going to plea guilty, and the prosecutor spoke up notifying the judge that they were going to file such an intent notice. The court DID allow Levi to withdraw his plea of guilty once he was aware that the death penalty was being sought.. but I do remember that they still left it up to him to decide if he wanted to change his plea. The court WOULD have accepted it after the intent notice was filed, if Levi wished to make that plea.
Levi did, however, change his plea to not guilty at that point.