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I can't see any reason to believe that the investigation has had any problems. The police have the obligation to investigate the crime, gather evidence, and forward it to the DA for prosecution. Releasing details to the public, and outlining their evidence to the public is not an obligation. It would seem that this is not a random killing, or something that is an ongoing threat to the public. There's no reason to be transparent, it will only weaken the investigation.
Sadly, the "botched the investigation" "clueless police" mantra is a tactic that defense lawyers have thrown out in every case imaginable, hoping it would stick. The tactic has succeeded in creeping into the subconscious, as intended. There's no video, no DNA? The police botched it. If the investigation has been thorough enough to involve the NYPD in cell tracking, I can't imagine anyone has been "had", or is clueless. Now, if the police were telling us exactly every shred of info they had, that would be clueless.
I don't know what LE has said or not said about whether the attack was captured by surveillance. If it were, that would be a good detail to keep private for a number of reasons. Revealing that you have that would light up a bonfire with the media. Any upside to that is not worth the circus of speculation it would cause. (not to mention the anguish this could cause family) It is not a matter of public safety, and the info from that video could be crucial in determining the truth in possible suspect statements later. The fact is that there is likely only eye witness to this crime. Unless the suspect has made statements to others, or the police, sustaining a conviction is going to take a lot of evidence gathering. Then, the DA is going to have to be satisfied, and file the case.
On top of that, when the case is filed, some lawyer will moan, "its all circumstantial..." Which is another misleading statement, as circumstantial evidence is actually more reliable and accurate than witness testimony.