I agree with Stew on the fact that a good physical condition will allow the person to complete their training with fewer injuries, but it also says a lot about a person who will put forth the effort to be as physically fit as possible and that usually translates to wanting to excel in every aspect of their training, making them a better soldier, police officer, or fire fighter, all of which are very physically demanding professions.
In my 22 years in the AF I found the Jocks who worked for me spent most of their time in the base Gym! Those who were very good at sports did not perform their jobs as well as their peers.
I am a former RVN veteran and a retired Cal state investigator that also had defensive tactics, police baton and firearms instructor duties for a good part of my career. Basic PT tests do matter showing physical maintenance and stamina is there for officer safety and that of the public. I noted in my state career that there are vast differences on agency fitness. The investigative suits especially those that do not have a law enforcement parent agency leadership feel they have different needs and even though they get equity pay, early safety retirement and adequate training funds they do not perform to basic-basic academy qualifications. It is for the most part the leadership to blame; I have had excellent leadership with most but as the politics of it all I've seen it go sideways with a change of administration & the bean counter attitude and philosophy of "we have different needs" and claims that "there is or you should always have uniforms or swat available...but that is not the real world. I have been shot at and assaulted with different impact weapons and it was the physical and equipment training that I credited to go off duty in one piece. I bring up my vet experience because in some hot incidents it was the lazy that could of and had got someone hurt. Thus basic PT tests do matter not only for officer safety but to protect those we suppose to serve.