Correct me if I am wrong. I think you have thought about this and studied it so probably have a better idea about it than me.
I think with the secrecy, law enforcement is usually trying to somehow protect their "case" for if it should ever go to trial and this protection comes at the expense of finding the killer. I suppose it makes sense in some ways because if they jeopardize their case but catch the killer, the killer might walk.
But it would seem that they should take that chance because finding the guy and losing the trial is better than never finding the guy. If they released everything they knew, somebody might put two and two together and realize that they know something and break the case wide open.
There are, over all cases in my database, several arguments LE all over the world raises in defence of this "secrecy strategy":
1.) Protect the investigation.
That one is bull because in fact, it is nothing else but the summary of their other arguments, so lets rather look at the real arguments.
2.) Protection against SCs
SCs are one nasty side effect of media hypes in serial killer cases. So-called serial confessors pop up and try to claim responsibility for the fifteen minutes of fame. In reality, this is a rather rare effect, but then serial killer cases are rare anyway. The parameters to know when one better calculates in possible SCs are defined and easy to see. The reasoning of LE is, they can only figure an SC by keeping some details secret. Well, they could also use whereabouts, timelines, profiling, but even if one says, details not known to the public identify SCs ... we talk about a little number of details, so this argument is effectively no reason to keep everything a secret.
3.) Protection of innocents
This was at least correct like 20 years ago. Today we live in the internet age. So there is no protection of innocents anyway unless LE says clearly, this person is innocent, we dismissed him as suspect because ... see CPH in the LISK case.
4.) Witness bias protection
One lawyer trick is to claim, witnesses recognize a suspect only because they saw them in the newspapers not because they actually saw them on scene. First of all, in all the cases in my database, I have maybe five or six, in which identification by witness played a role. And I have some hundred in my database, the 25, I show on my website are only the peak of the iceberg. Second, the moment, LE makes an arrest, the photos are anyway in every news outlet, which leads this argument ad absurdum.
5.) To keep the perpetrator in the dark where the investigation is going
Another bull****-argument. LE, bound by all the textbooks are so obvious, to predictable, nobody needs the news to figure what they are doing. To make the problem worse, the BAU (to be exactly BAU-2 and -3) are plundered by counter-terrorism. Means, most current profilers working there have the textbook experience from the academy at Quantico and maybe they read Ann Rule. Well, at least that helps to undertand serial killer cases a little. Much more than what I could recently find in the FBI whitebooks (which reached as of yet unbeknown levels of clichees and platitudes about serial killers). So what was once the craddle of serial killer hunters, the holy grail of profiling, degenerated during the last decade to a kind of rubber stamp profiling factory. The absolute low point was the rubber stamp profile of a white loner in mommy's basement in the case of the Baseline-Killer. When they published their white loner, already three witnesses had stated, the attacker was black (the Haiti-variety, not the Africa one). So, all of that makes them more predictable than a can of soup and therefore, the argument, to keep anyone in the dark, doesn't pull it off.
There are however, some real reasons:
1.) Serial Killers aren't good for tourism
Which is, why every SK case in any area with tourist industry basically puts immediately political attention behind the scenes. And the orders are clear. First they say, no SK is around. And if they can't deny it anymore, they have to play it down, to prevent panic. Which is kind of a joke, we get ten SKs weekly in TV, they have become part of our life anyway. But the same argument weighs in even more when a tourist is killed. The Freeway-Killer, Bonin, since there were three with that nickname, killed a German hitchhiker as one of his early victims. It took weeks till they even told anybody that this one belonged to the same series even they know immediately. Bonin and his cronies had made sure, there is no mistake possible.
2.) SKs make PDs very nervous
All PDs have still this outdated idea of the homicidal genius who knows no fear. Like Hannibal Lecter. There are bright ones, there are really dumb ones, most SKs are rather in a normal IQ range. However, what started as a convenient story, LE told the public to look better if they catch such a guy and to look less bad if they don't, it became the credo for the next generation of LE. They actually believe in the political correct lies of their seniors. And since they assume from the start, the chances to look good in such a case, they start covering up for possible theoretical failure before they even start to look for the killer.
3.) Competition makes PDs nervous
For a PD's public relations department, only one thing is worse than not catching a serial killer. If someone else catches him. Because people ask, why the guys paid for it, can't do it. So protecting the investigation means often protecting it from competition.
4.) Inbred estuary behavior
The keyword is jurisdiction. Every detective knows, where his jursidiction ends. But inside that borders, he is the one, the big cheese, numero uno ... you get the gist. And he will bite everyone, who comes from the outside. Public, people like we here, we are outside.
5.) The Jerry Bruckheimer Syndrome
Everyone thinks, police labs have all those tool toys like in those shows. They don't. Still, they have a lot of tool toys. And the normal police detective believes in those toys. They think in categories of "we have" and anything alese is "amateur". The BAU fights often enough to make PDs even reading their profiles. Because Detectives think, this is just blah and we have DNA now. Well, to use DNA, you need someone to compare it in the first place. And when the whole investigation runs cold because they can't find someone to compare it to, someone has to be blamed. Nobody wants to be blamed and therefore, return to 1.).
If you read the cases on my website, you can see, it's not new to mess up SK cases. I am not so much in single murder cases, so I can't say for sure, whether all of this applies there, but I strongly suspect it. I looked lately in some cold cases. I sit on one, 60 years old, where a suspect is pretty well connected and pinned down (which doesn't matter, he is dead anyway). Only one thing is needed to close the case. One piece of evidence. I know where it is, but I can't get there. Clearwater County Sheriff's Department. And they "can't" release evidence. They don't even return my calls anymore. Because if that case would be closed after 60 years, people would start to ask questions. In another case, I work my way through, the wall of silence, LE put up is far higher and much more impenetrable as the law of silence in the mob. Compared to the average Sheriff in some parts of the country, a drug dealer or a killer is usually a pretty verbose personality.