I don’t think its a matter of her being a D throwaway, since she’s had no previous elected office and presumably would not. All the others are in elected office and likely want to continue on that path. Not so Rice.
They don’t care about Rice’s future elected political ambitions. She could be easily thrown away and not affect the party’s top ranks such as a Kamala Harris might be ruined, should she be chosen and lose bigly.
It’s actually a game of chicken, rather than cat & mouse.. If Ds go first, appoint Rice, Rs indict 1/2 of the ticket. If Rs come first with Durham indictments Ds can avoid Rice if she’s indicted, or proceed with Rice if she’s not.
Each is waiting for the other make a move, thus delays from both camps.
Rs will win this one, though, because Barr/Durham & Rs can outwait the Ds with their convention near.