A defendant always has the right to plead guilty before trial and, I suppose, at any point during a trial.
Generally a plea agreement is brokered, usually the Prosecution and the Defense getting something and giving up something in the process.
IMO the State doesn't have a reason to give up anything, they've got full confidence they can convict on full charges.
Therefore, there's nothing of value (for the State) for BK/the Defense to give.
Now, if it was a shaky case and the State needed, say, the murder weapon, or the name of (if something like this were the case) another, more involved perp, or where the bodies are (huge bargaining chip in cases with missing persons) but the State appears to have everything they need to secure a conviction without any help from BK and his side of the courtroom.
The only possible thing is the DP, whether it's on or off the table.
For whatever reason, however, I don't think AT signed on to negotiate a plea -- probably because IMO BK either isn't talking or said no (I suspect he has said a total of zero words about the crime to his attorneys. BK's rich conversations happen only in his head IMO.). She came to play ball, intent on making the State hit hard. She don't let them convict with ease.
She seems to be borrowing from the new defense manual -- play to the public. Because that's where the future jury sits.
It'll be a fiery trial, no doubt, but IMO the State has the goods.
When they lay it all out, end to end, at trial, BK will be staring at a home video, a reel of every terrible mistake he made that day.
JMO