To be fair, the amount of effort involved in verifying every little detail a witness/victim/subject provides is astronomical, not to mention the potential for a defense case based on the lack of effort to verify one fact when other facts were verified.

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.