Either he is in charge and makes the decisions to hire and fire or he isn’t!
It’s really that simple, he’s responsible for this mess and if he thinks this coaching staff should continue, then he is not fit for this job or was hardly ever in charge to begin with.
What is the benefit of firing them now? I think you’re better off keeping them and then fire them at the end of the season. Can you help me understand why you believe they should be fired right now?