He can report a nurse. It then has to go through investigation and proper policy and procedures.
They have to follow staff procedures.
That's what he/they were already doing.
But they were being delayed, given the runaround and obstructed by management.
While the unexpected and unexplained collapses and deaths continued happening.
By the time he directly asked the manager to move Letby, they'd just lost two babies who weren't expected to collapse or pass away. He was utterly desperate.
He seemed to think he had the power to get her moved off immediately on his say so
He didn't think that, he was explaining his concerns and the urgency of them to the manager and asking her to move Letby or he couldn't take responsibility for what would happen next ....when she wouldn't.
He asked her in utter frustration and desperation, would she take responsibility if another baby collapsed or died. She said yes.
But she hasn't.
I find your interpretation of his behaviour very very odd.
(And incredibly unfair to him).