We should not - it's a dangerous idea which gets people's lives destroyed. "Innocent until guilty" is an important concept which mob justice often forgets which causes a lot of damage.
Just because one system is broken, doesn't mean that we have to replace it with another broken one.
Does mob justice have a wonderful track record? Just because police and justice system are not perfect doesn't mean that the "alternative" is the one that should be considered right.
Just because one system is broken, doesn't mean that we have to replace it with another broken one.