The alternative is therapy and love in a safe and stable environment for people who have a realistic hope for improvement. Any other solutions are bound to fail. It is also a matter of mentality. The knights are prepared to accept some failures if they can save someone, the white council is prepared to kill more people than necessary to be on the safe side. And they don’t want to spend the resources.
The Knights don't have to worry about Fallen summoning He Who Walks Behind. You cannot make a fair comparison because the threats, and circumstances are completely different.
Harry required years of constant supervision from someone. The Council actually gives this option to wizards. Most are not willing to look after a potential warlock because they know two things:
1. It really could get them killed.
2. Their failure would mean innocent people die.
It would be like willing to go to sleep under the same roof as a possible serial killer. How many want to take that kind of gamble? Would you?
The most dangerous people wouldn't be the frothing at the mouth, obvious warlocks with no hope of redemption. It would be the ones who you aren't sure about. Those are the ones you have to worry about burning you alive in your own bed after a nice dinner.