You need to read Batman White Knight. That deals with the whole concept of whether the Joker can be redeemed or not really well.
Imo it doesn’t matter whether or not he can be redeemed. He’s killed so many people that his life is forfeit
That’d be like saying Hitler or Stalin were worth keeping around because their multiverse counterpart was able to do good.
I mean, I don’t believe in caltial punishment so I’d disagree with the “life being forefit” idea in any sense.
The book deals with the idea that the persona was a mental illness and with treatment he becomes a useful member of society again actually entering politics and improving the city.