It never made sense to me why he was wandering around the city in the same exact clothes he used during the murder. If he had simply worn another jacket, he may never have been identified. How could he not have realized he'd be on camera or described by witnesses?
Now he gets caught with all the incriminating evidence you could ask for? I'd say Occam's Razor points to your second theory: He's not playing some sort of 4D chess. He just decided to go kill this guy for some reason and went and did it. Dumb luck and a dense population easily explains how he was able to escape the city.
That's the part that baffles me. Whenever something like this happens I re-engineer the planning as a mental exercise. I have never had any interest in offing anybody, but I never understand not having a plan and a basic disguise. The guy had IDs, but he also did nothing to hide his p[articular characteristics. If he had thinned his eyebrows and worn fake glasses and kept his mask on he'd likely still be at large. I would have ditched or reversed the jacket right away and thrown on a hat at the very least.
I think it is more informative to think of a time you planned a big trip, especially if things went really wrong on the trip or there was a significant problem. Looking back with hindsight, I can see how I may have failed to see and adapt to an issue before it got bigger or that I act irrationally because I’m stressed and I haven’t let go of a preconceived notion and accepted the new situation. I have wondered why I didn’t investigate something beforehand that now seems obvious and important. There have been cases where sheer dumb luck saved me or screwed me. Afterwards I could say I should have had a backup X or should have planned Y ahead of time, but I didn’t see or do those things.
There are so many moving parts in a situation like this that it is impossible to think of everything, and the things you don’t think of will look obvious to people after the fact. The dumb luck situations that save you or screw you can be interpreted as inside knowledge. His bumbling actions afterward from the outside might seem like a “why wouldn’t he just do this instead” without thinking about how the mental toll, stress, and panic of being hunted by the whole country could degrade your judgement.
My guess is he didn’t spend a lot of time thinking about his emotional state after pulling the trigger. He probably immediately regretted the decision and half heartedly followed some sort of escape plan.
Now he gets caught with all the incriminating evidence you could ask for? I'd say Occam's Razor points to your second theory: He's not playing some sort of 4D chess. He just decided to go kill this guy for some reason and went and did it. Dumb luck and a dense population easily explains how he was able to escape the city.