No Body, no DNA, no witnesses to interrogate, no proof the guy even existed!
I think all the cases this detective had dealings with should be reinvestigated immediately.
Sadly, for your argument, there is sufficient independent (non-Biblical) evidence to indicate that someone of the name and actions reported in the Gospels existed - possibly more than for many other person of the time. The sticking point is the supernatural element of the story. By the way, there woul;d seem, according to Wallace, enough eye-witnesses to interrogate - and he did so.
As for opening the cases again, it wouldn't have been him alone - he was part of a team as far as the other cases are concerned so anything out of the ordinary that he might have come up with would have been double- perhaps even triple-checked already.