Death penalty

Suicide is murdering yourself. Many Christians and possibly other
groups are strongly against it. It's also a way to escape
punishment, scorn, and harassment from the courts-are-perfect
believers.

Exiling only gives another place the problem (should the person
actually be quilty in reality and is inclined to repeat the crime).

You need to be able to let the person go free should it be discovered
later that they were actually innocent and did not commit the crime
at all.

You can't let the person free if you killed him and the leaks of the
person's innocense, if he's discovered later to be so, doesn't make
the legal system look good at all.

George