I think when the rage dies down they experience an “oh oh” moment. Eventually, of course, they get caught.
After locking up someone for killing out of revenge, even if they have a death sentence, a person remains in prison for many years where some inmates “find God.”
Most inmates say they regret what they did, either because they now realize it was wrong or some because they got caught. The vast majority swear if they could they turn back the clock they’d not do it again. Some claim they didn’t kill anyone and they were locked up by mistake.
Once in prison, inmates are not treated differently due to the crime they committed but by the way they behave with other inmates and prison staff. A well behaved prisoner gets more privileges, like being able to walk to the chow hall on his own. A badly behaved prisoner is often put in more and more restrictive custody.
There are inmates who murdered someone for revenge, received a life sentence due to a plea bargain and walk to the chow hall on their own, sweep walkways or repair plumbing. Some of them work in craft shops where they make items out of leather that officers can purchase, like holders for the C.O.P. gas (mace carried just-in-case). The money is placed in the inmates trust fund (they never see any cash) so the inmate can purchase items from the prison commissary like chips, soda, candy bars, Raman noodles, postage stamps, typewriters and art supplies. Some of them get regular visits from family members who also deposit money in their trust fund.
Inmates in Texas, some of whom murdered for revenge, make all of the license plates for vehicles in Texas and several other states using special machinery.
Thousands and thousands of people in every state are employed and make a living caring for inmates in prison. These include correctional officers, nurses, doctors, psychologists and administrative staff.
After locking someone up and throwing away the key, life does not end for them. It just changes.
This gives lots and lots of time for the person who can’t leave time to think about what they did and what they could have done to prevent it from happening in the first place.
To answer your question, therefore, if you kill someone because of rage, you might feel good in the moment, but then reality sets in.