It's September and after a nice, long vacation, school's back in session. Let's learn together!
Here is the reasoning for it
Unlike citizens, cops don't have the option of not cooperating or not giving a statement.
First, let's get a couple of things straight: The Fifth Amendment extends to everyone under its jurisdiction; that is, it extends to citizens and non-citizens alike. You likely meant to say "civilian" (a dreadful reminder of how militarized your profession has become), but even that would be wrong: the Fifth Amendment does not make exceptions for cops. The Fifth Amendment begins with "
No person shall" and it doesn't include an exception for Cops.
So your statement is, to be blunt, false: nobody can be compelled to testify against themselves. The Constitution is the supreme law of the land and it firmly establishes our right to not answer any questions. This means that a cop could opt to invoke his Fifth Amendment right against self-incrimination to not write the report and not answer questions. He'd lose his job, probably—and that's how it should be—but he could not be "compelled to cooperate and give statements and answer all the questions" anymore than any other person can be.
Over time, history has shown that statements taken immediately after a traumatic experience aren't always as accurate as statements taken when a person has had time to calm down and reflect.
That seems reasonable. Tell me, if I accidentally walked into the wrong apartment and shot my neighbor, would I be allowed to go home for the night to "calm down and reflect" before I would have to come down to have a nice friendly talk with my coworkers?
If accurate statements are what's important and we know that people are unable to give accurate statements in the immediate aftermath of an incident—which does seem at least reasonable—should we not afford every the same courtesy of a cooldown and reflection period to everyone? Because, surely this inability to provide accurate statement isn't something that only cops, right?
Yes, you could say they can also make up a story but that's not an overwhelming reason to get what will likely be an incomplete statement right away.
I could also say that time appears to be of the essence in every other investigation, except when cops are involved. I could also say that it's better to have as much information collected as soon after the incident as practicable, and allow for follow-up interviews, as necessary.
And a citizen correcting their earlier statement isn't viewed in the same light as an officer correcting an earlier statement.
It isn't viewed in the same light as who? Any such statements would almost certainly not be released publicly, at least until the case goes to Court.
So, you're suggesting that cops would be more understanding of a civilian who corrects his statements and less understanding of a cop? You realize that's just laughable right?
And, beyond that, if the cops make inferences because someone corrects an earlier statement, having taken time to "calm down and reflect", then what does that say about your brothers in blue? You just told us that history teaches us that taking time is good because it helps people make more accurate statements. Are cops unaware of the teachings of history?
The latter is automatically viewed by many in the public of being a part of a cover up or lie. So they are given 72 hrs to collect their thoughts, review their reports and give a complete statement.
And do you blame the public? Not a day goes by when cops are caught in blatant lies; check out for one
particularly egregious example.
Oh, and while we're here, how is the former viewed cops and ADAs? "Oh, good, the suspect remembered more details which help us clear him. Imagine if he hadn't; we could have put an innocent man in jail!"

I can tell you that there were times when I was involved in an incident I thought X happened. For example, after a shooting incident and chase (not an officer involved shooting) after catching the shooter, adrenaline was high it was a chaotic scene. I remembered putting the suspect in my partners back seat. Would have sworn to it. When I watched the video, I was surprised to see that shortly before we walked him to the street, another unit had pulled up and that is the car we put him in. Small thing, but certainly could have been made to look like I was lying.
It's one thing to be mistaken about which unit you put the perp in; after all, all cop cars look alike. It's also something that's largely inconsequential (thought I'm sure an attorney would relish the opportunity to grill you over it in front of the jury to gain some points).
So yeah, officers get 72 hrs, but, they are also compelled to cooperate and give statements and answer all the questions.
Yes, cops have to write reports about incidents they are involved in
in their official capacity as cops. Airline pilots have to write reports if they declare an emergency, or they dip into their reserve fuel. University instructors have to write reports when a student complains about a grade. Doctors have to write reports after they finish giving your prostate a thorough tickling.
But they can't be compelled to testify against themselves. The Constitution is the supreme law of the land and it firmly establishes our right to not answer any questions. This means that a cop could opt to invoke his Fifth Amendment right against self-incrimination to not write the report and not answer questions. He'd lose his job, probably—and that's how it should be—but he could not be "compelled to cooperate and give statements and answer all the questions" anymore than any other person can be.
See the first part of my answer if you need a refresher as to why that is.