Random fun thought experiment for my sake for a potentially better reason,
I presume the cop died before you got the suit(*body) to John Doe, so you could reason the suit had already send out the ping to the overarching network (Whether local or global, depending on if it still exists at all) as a "Hey, this guy died" thing. Now it's cut off/burned through any of the usefull tech on it to try and prevent repurposing.
Additionally, the suit is likely wrecked/torn up from having suffered enough damage to kill the wearer that it is better to replace the suit with something else. You are effectively risking being wrongfully identified by your friends as a cop by wearing it with little added benefit to off-set it.
Finally, depending on how far you want to push it/how involved the overarching network (be it AI, Dispatch, Overwatch or some other force) is in managing/monitoring data, having a unit get reported as KIA along with most/his entire team and then later, without getting info that a suit has been recovered, having that same unit suddenly either report itself as possessing some form of vital signs OR, again depending on how far you push it, suddenly get up and start moving again.
The latter being potential reasons for interest from Overwatch/The Combine-side in figuring out what happened, attempting to get their soldier/cannon-fodder back. Which could be either reasoned as John Doe or some other rebel that, unless there is a specific plan in mind to utilize the situation to achieve a goal, it's better to just ditch the suit somewhere and get some rebel gear instead (perhaps scrapping parts of the CP suit to make such a rebel suit)