It seems far more likely to be a case of incompetence. Law enforcement actually has an extremely low rate of "solving" cases, especially if you exclude all the "solved" cases where the suspect is caught on scene or that end in a plea bargain (i.e. did not have to establish sufficient evidence in the first place).
Ever since he got "caught" (if you can call someone literally telling the police where he is "the police catching him"), all I've been hearing about is how the police wants to use DNA evidence and bullet "fingerpints" (i.e. attempting to demonstrate that a bullet was not only fired from a given type of gun but a specific singular gun of that type) and other CSI woo to now tie the actual crime to him. They might actually be lucky and produce matches in this case as they have the actual suspect and murder weapon (assuming this wasn't an extremely unlikely 5D chess move of using a body double fall guy and/or different gun) but both of these types of evidence are extremely unreliable and rarely help actually finding the suspect even if they make for good television when they work. As I understand it the police even walked back on the mayor's initial claim about "having a name" to "having a list of names" - not to mention that you don't call in the FBI when you already have good leads yourself (if only for optics/political reasons).
He seems to have been mentally unstable for a while before engaging in this killing and the fact he wrote a manifesto strongly suggests he had an intention of being caught or at least considered it highly likely. The monopoly money bag wasn't necessarily a "red herring" as everyone I heard talk about it interpreted it as intending to send a message, which seems to agree with the apparent contents of his manifesto (based on what news reports have cited from it). The water bottle the police now wants to use for DNA evidence may have been deliberately left there for this purpose, too.
Based on what I've heard of his manifesto, he may have intended to kill other people too but have realized the difficulty involved given that his very public first killing likely spooked the other people on his list. I think it's more likely he didn't fully plan out an entire sequence of killings or didn't account for these complications and essentially gave up, settling on being caught sooner rather than later. People generally don't write manifestos when they don't also want to take credit for their actions.