The problem is that he could also probably use a federal immunity defence. The prosecutors need time to plan out a good way to attack this defence. The worst possible outcome would be to file charges now, unprepared, and then the guy gets acquitted at trial which forever bars future state prosecution for that offence, or the case is dismissed because prosecutors failed to present a good argument for why the accused is not immune. Prosecutors have only one chance so they tend to make sure their case is as good as they can get before shooting their shot.
It's actually very rare for murder trials to be argued over whether the accused killed the person in question. Usually, the argument stems from whether the killing counts as murder or whether the evidence that the accused killed the victim is legally admissible.
He will still try to argue that, and prosecutors need to come up with real reasons why it doesn't apply. Defence lawyers are not stupid and they will probably think of a way to argue immunity. Those arguments must be anticipated, researched, and rebutted.