It is useless to have guards that hunt killers.
As is any such system inefficient in reality it will also be inefficient anywhere else.
The problem is that if you do not want to be attacked or killed it is not satisfactory that the character that did it is killed as well or jailed. You were already killed after all. And they can create a new character anyway.
In reality we cannot prevent that but in a game world it can be prevented and so it should.
The option to engage free killing would be nice as such play is more thrilling. And it relies more on good use of chracter abilities than the stuff you carry as you are not likely to carry it for long, obviously. And carrying good stuff atracts thieves as well.
In this case guards can be part of the setting. But they should try to kill offenders because they are guards and it\'s what they do (similarly to creatures that try to kill anything that moves). It\'s not like killing another character is a problem. Just get out of sight or kill the guards as well.
But it also gets tiring if you try to play a peaceful character and have to defend from assasians and thieves all the time.
So in my opinion it is primary that the world is mostly safe.
Arenas and parts of map (preferably with towns and everything) where killing is alowed are nice but not strictly necessary.
Also allowing killing outside of towns is not a good idea. Killers could make exploring the world impossible.