People who have life sentences overturned are incredibly rare today though and likely to be rarer in the future with current advances in DNA profiling and forensics in general. When it does happen it's great but the person has usually spent most of his/her life in prison already, so justice not done as the real killer is still out there. This is the flip side to the executing the innocent argument. It's also why America has Death Row. It' gives the accused perhaps decades to make successful appeal. Take a look at one the America's most infamous serial killers, Richard Ramirez.
23 years to get his conviction overturned and it still wasn't long enough to send him to the electric chair/gas chamber/lethal injection.
He was 100% guilty but managed to spend 23 years of tax payers money on appeals and incarceration fees trying to get off. Instead of bottle necking the justice system with people like him, they should have just executed him.
So there are cases for each side. Maybe the lesson is there is no absolute fix and so logically a combination of the two is the right approach.
Or more rationally, instead of spending so much tax payers money trying to kill someone they should have locked him up in a cell and thrown away the key, metaphorically. Would be much cheaper and more ethical.