But even then, talk to an attorney if you want to confess something and he will tell you how to do that. I dont know the situation in the US, but I would assume it would also involve the prosecutor instead of the police.
Some people feel guilty after committing crimes and turn themselves in. I'm asking on behalf of those types. Why is it a bad idea for them to just show up at the police department and confess?
(The police & prosecutors will try to pin as much as possible on you. It's all about those numbers.)
You may feel guilty, but not enough to commit seppuku. So you can at least request your mortal body not be placed in the local hellhole prison, get a more reasonable sentence, etc. This is done by having a lawyer negotiating on your behalf.