I believe the death penalty should be abolished anyway. But, disregarding the complexity of the implementation of such a policy, if the government is in the business of ending people's lives, I'd rather it be done to directly help people, instead of in a punitive fashion. If you think about it, the death penalty isn't really a punishment - some people commit heinous crimes specifically so they can be killed.

"Suicide by Justice" doesn't seem like it would be or is a popular enough form of suicide to warrant what you're suggesting. Your logic doesn't make much sense.