I know this is a long excepted view, but there is no logical merit in it. When a "price" is paid, it is paid to someone. Who get's paid by someone's death, or even someone's incarceration. Both of these impose additional cost or penalty on the victim.
If you mean, by "price," that all actions have consequences, and it is up to the government to make sure bad actions receive the consequences they should, most governments are generally in the business of the opposite, making sure people do not have to suffer for their bad and stupid acts. In fact, it is usually the innocent that have to pay to support the evil.
Justice should always require restitution to whomever a crime has been committed against, where possible. Where this is not possible, because there is a death, or the thing harmed is irreparable, then death is the only alternative. If neither of these is possible, (or allowed), any other action can only make matters worse.
As for, "you are not trying to teach the dead you're hoping to teach the living:" What are you trying to teach them. The living, we presume, are the innocent, those who have not been convicted of crimes. Why should they be taught, and what does watching (or knowing people are bing killed for breaking a government's laws) teach them?
I know these views are different. How is the justice system based on prevailing views working?
Hank