Note that it's not the police's job to think or not to think about motive - that's the job of the DA. For a reason - law degrees among other things.
Wrong. The police who investigate crime look at motive, means, and opportunity. It's their job to follow the evidence. Not to make the evidence to fit some political agenda.
My impression is that mistakes are made when they settle on a suspect prematurely; then only look for evidence to make their case.
In this case, they know who did it. The young man confessed and told them why he did it. Apparently, some people who never talked to the guy think they know better. One blogger was even po'd that the police arrested him unharmed.