Unfortunately, I don't have faith in all defence lawyers to do this kind of thing - some "free because you're poor" lawyers might spend only 20 minutes per case...
Another possibility is that the investigators fail to share evidence as required.
Imagine a murder case where the accused claims he was at the cinema at the time. Often the police won't go to the cinema and get CCTV tapes to back up the claim - they'll just use blurry footage from the murder scene and claim "looks kinda like the same guy ish".
I suspect there are a lot of cases of innocent people in prison simply because evidence of them being innocent was deliberately overlooked or not collected.
A woman was found murdered in a cemetery. She was in town for a university-related festival/party, and was staying temporarily with some other students.
The police suspected the other students first, and went to their house, and found out:
1. One was an RPG player, had RPG books.
2. The other was a heavy metal fan and had heavy metal-related posters.
3. The other guy was into literature and had some 'dark' literature.
So conclusion of the officers: it was a satanic cult, and the woman was killed in a "RPG Satanic Ritual"
The prosecutor's office at first went with it too.
Later, already mid-trial, the prosecutor changed, the new prosecutor found a lot more formerly-useful now useless evidence that the police seemly deliberately ignored:
1. The police had in evidence storage some bloodied clothes that they never ran DNA tests on, the DNA was now useless (it has been years since the actual murder). Also the evidence was probably contaminated, the storage consisted of stuffing all the evidence in trash bags and leaving them in a random room in the police station.
2. People told the police multiple times, that the woman had drug debts, but they were ignored.
3. A known drug dealer was seen on the day past the murder, riding a bike around town, with his t-shirt having red stains on it, police even seen the guy themselves, and didn't bother stopping him and checking his t-shirt.
The new prosecutor despite seeing all this, had hands tied and just went along with what the police wanted, and tried to prove in court that they were "satanists".
The ruling was this (the judge was quite upset at it too):
1. The prosecution failed to prove they were satanists, evidence pointed out to the accused living there by coincidence, and their hobbies being "dark" or "fantasy" were coincidence too, only one of them was an RPG player, only one of them was a heavy metal fan, and so on, they didn't shared their hobbies with each other.
2. And even if they WERE satanists (they weren't), in Brazil being a satanist is not a crime.
3. For some reason the prosecution provided zero evidence that was actually related to the murder, they only tried to prove the accused were satanists and presumed this would be enough to know they were the murderers, but they never tried to link the accused with the crime scene, didn't even tried to explain when they would been at the cemetery.
In my old agency, we were required to do that type of thing. For example, we had a rape case where the rape occurred in a short-stay house (kind of like a hotel, but for families that require room for multiple kids/pets, etc). The subject only rented the house for one night, and the rape occurred in one of the bedrooms. By the time we got to the house, there had already been another guest for the night between him checking out and us arriving. We went to housekeeping and interviewed the staff who cleaned the room, we dug through the trash to verify the drinks the victim claimed to have drank, we got camera footage from the gas station where he bought alcohol (she was also underage). There's a ton more that was done to verify key facts, most of which were essentially meaningless, but we did them because we are required to.
Now, imagine if a victim tells you a story that includes 10 things that could be independently verified (through searching a location for CCTV, pulling receipts, whatever) and you only look for 7 of those things. This opens up the defense to make an argument that you intentionally skipped looking for those other 3 things because they were exculpatory. It's impossible to think through all the different details that could be verified, along with their probative value to a case, and organizing them by how long you have until the evidence is no longer available (there's no standard timeframe for how long before a given store's CCTV recycles).
I'm not saying investigators shouldn't do this ground work, but I am saying that it's a shitload to ask of them and potentially opens up the prosecution to a very bad-faith defensive argument that certain seemingly-obvious factors weren't considered during evidence collection.
In your murder example, sure, they could say "looks kinda like the same guy ish" and hope that's good enough for a jury, but the defense can (and should) tear that to shreds. If a subject told us they were at the cinema at the time of a murder, my first thought would be to ask them to provide any evidence they themselves have (social media check-in, location data from their phone, receipts/credit card statement, etc), but I would also absolutely be checking the cinema for video evidence. If I can prove he lied, that's a huge win for the prosecution. Alternatively if he's telling the truth that he has a verifiable alibi, then the real killer is stacking up time while evidence entropies.
The reality is that cops are burdened enough that the only evidence that's persistently worth verifying are usually statements made by subjects. This is where case where it's worthwhile to talk to cops: if there is potentially verifiable evidence of innocence that stands a good chance of diminishing as time goes by. Giving specific details like the place and time that you saw a movie at a theater along with any receipts or ticket stubs, would be a huge factor in preventing future law enforcement / prosecutor interactions.
This is only true if the cops are actually looking for the Truth, not just a way to close the case as fast as possible.
You seem to have faith that the cops / prosecutors are attempting to find the truth, unfortunately I do not share your faith in the system. So the better plan, for your own personal safety, is to NEVER TALK TO THE POLICE [1]
Might want to think twice about that, you might be replacing one allegedly innocent suspect with a suspect you know for a fact is innocent, yourself.
I recently witnessed a case where a trooper charged the wrong statute. How can you make a thorough investigation if you don't even know the elements of the offense because you are looking at the wrong statute?
He made about 5 other mistakes too, even lying to the judge. The system doesn't care. The investigation into the lie was found to be a "just a misunderstanding" eventhough that same report also notes that the statement was false and that he made the correct version of that statement 10 minutes prior to that.
They also don't maintain good Gugilo records. You can request that information, but they won't give it to you because they don't keep good records of the past issues, on purpose. I had a trooper contradict himself in court and official reports 3 or 4 times. The prosecution still found him to be a reliable witness. Anyone else would have their testimony thrown out.
Because they don't keep good records of these contradictions, I guarantee future cases requesting this information will not get it.