That's a common tactic to try and get a suspect to turn themselves in.
Sometimes it works. (Most suspects turn themselves in for crimes they've committed. It's actually the exception when police need to go out to arrest a criminal suspect.)
Sure, for nonviolent criminal offenses. It helps that accepting responsibility for one's actions (as demonstrated by turning oneself in) generally results in significantly reduced sentencing.
For violent offenses, and especially for high-profile murder cases, they don't give the suspect the option of turning themselves in.
> they don't give the suspect the option of turning themselves in
That seems a lot like the responsibility of the suspect? Like, if you're planning on shooting a high profile target in midtown Manhattan isn't the exit something to think about? Based on what information we might actually have, the shooter had plenty of carelessly missed opportunities to not be caught. Poor planning, in retrospect, is a choice.
Sometimes it works. (Most suspects turn themselves in for crimes they've committed. It's actually the exception when police need to go out to arrest a criminal suspect.)