A bird in hand is better than 2 in the bush.
I'm quite convinced that police frequently fear searching for the truth about suspects when the truth may point to another person. This means that doing more investigation would inculpate another (uncharged) person, while exculpating the charged person. Thus, any work they do undermines the case they have, for the hopes of building a case against someone else. However, if they were to ever file a case against that other person, the person they previously charged looms as reasonable doubt in their case against the new person.
What this means is that they would prefer to just go with what they have, since further work may bring up information helpful to the suspect, and they wouldn't want that.
Naahhhh, you say, this couldn't happen in real life. Except for a murder case I have right now, and a murder case I had in the past.
In my past case, the police failed to follow up on a suspect, someone ID'd at the scene by two of his "homies," because that person didn't fit into their theory of the case. They claimed not to know who this person was, so I even gave them information on this person, including a photo. They never even drove by his house. You have no idea how nice it sounded in trial, when I cross-examined the detective on 4 different days during trial: "officer, you have had this person's info for 9 months now, have you bothered to go to his house yet?" "Officer, how far do you work from his house?" "Officer, have you even bothered to call his house?" "Officer, have you even bothered to run him for priors?" "Officer, you work 5 minutes from his house and don't have to pay for parking, you can even park in a red zone in front of his house, have you bothered to do this yet?" "Officer, you could go to his house today after trial and still be home by 6:00, is that right?" "Officer, it's now 3 days since I asked you these last questions, have you bothered to go by his house yet?" "Officer, you've been back to the office now 5 times since we first spoke, have you bothered to go to his house yet?" When that was read back to the jury (at their request), it sounded devestating - Not guilty.
Now I have another one where the police stopped investigating one suspect (someone a witness ID'd as being the shooter, who later lied to the police about his whereabouts that day, and then moved out of his adjacent house 2 days later) when they got another suspect who 2 witnesses ID'd (that would be my client). My client requested that we DNA test any and all evidence that the shooter may have touched (knowing that the DA and police would do so before we could, would get the results, and would use it against him if it came back positive), and VOILA, samples were recovered that excluded my client. So, the simple thing seems to be, get the other person's DNA, right? Oh no, we couldn't do that now, could we. That would only mess up their case against this defendant. So, now I'm going to have to somehow get it. Incredible how many less resources and abilities I have to do this than those with badges and guns.
Just remember this when police and DAs insist that it hurts them just as much as the defense for someone to be wrongfully convicted.