Well, Cole does kill quite a few people and he gets away with it. Honestly, "I'm sorry and I won't do it anymore" really doesn't cover it.
Cole's arc in Asunder is a tad muddier of a situation though.
While it's true that he believed that he would fade away if he didn't kill people to stay "real", something that is obviously wrong and which he shouldn't of done, in reality, what was happening is that he was subconsciously seeking out people who desired death and providing a mercy-killing to end their suffering. In that way, he was fulfilling his role as a Spirit of Compassion, although not in the manner he should be.
It's why he admits he was a demon (or close to becoming one) at the time, because as Solas notes, a demon is just a Spirit who has had their cause and purpose perverted and twisted, turning them into the opposite of what they should be.
He continues destroying people's memories unless the Inquisitor sets him on the human path. He can also destroy Inquisitor's memories of him - in case you decide to not take him into the party. Erasing your memories and interrupting the stream of your consciousness is very akin to death to some people - to me, certainly, it's not unlike murder.
Except that Cole doesn't know how to stop people forgetting him (something that distressed him constantly in Asunder), so it's hardly his fault that he's passively erasing himself from people's memories? While what he does is technically mindscrewing people, it's not done in a malevolent way or intended to cause harm to them.
Think of the last time you stopped and asked someone for directions? Or a stranger helped you out? You can probably remember the event, but can you recall their face exactly? Probably not, because that information is not crucial for your mind to retain, so you tend not to? Cole seems to do the same thing when he makes people forget, so that people recall (on some level) being helped and that small act of charity, just not who peformed it?
He also torments people by spilling their innermost thoughts in the presence of others, which is painful, tactless, and again, he keeps doing it. Only in the human path he realizes that some things he might've said were wrong, and even then, those banters keep happening.
Cole never does this to torment, he merely voices things that people are keeping hidden which are causing them pain, in an attempt to try and help them. Besides, this ignores that Spirits and Mortals are two very different kinds of beings with different thought processes.
Spirits keep themselves relatively simple and avoid learning anything outside their task, to keep themselves pure. When it comes to dealing with Spirits, you always know what you can expect, because what's on the surface is all there is?
Mortals on the other hand are complicated and tend to internalise their feelings, motivations and secrets, so what they are saying and what they are thinking can be two entirely different and contradicatory things.
The concept of privacy is not something he's used to and indeed, the idea of keeping painful memories hidden would seem downright ludicrous to a Spirit because why would any sane being want to continue living in pain and hurt, rather than deal with the problem or let anyone help them?
He is also rather quick to judge - he finds no redeeming qualities in Erimond, he kills Seeker Lambert and never regrets it, and, basically, he remains a killer who is glad, willing and able to kill to help people. I rather prefer Solas' view - only kill out of necessity and when there's no other choice, and even than it's a sorrowful affair.
To be fair, Erimond was pretty irredeemable because he was perfectly willing to sell out the entire world for his own benefit, murder innocent people and bind an entire army of spirits and demons into servitude (I say Spirits as well, because Solas' quest shows how easy it is to pervert a spirit into a demon if you force it to go against it's purpose)... and showed absolutely no remorse for any of his actions afterwards?
As for Lambert, he killed him because he knew that he was never going to give the Conclave a chance and was always going to purge the mages. However, he does have a lot of banter with Cassandra where he reflects upon what he did, eventually realising that it possibly wasn't the right thing to do. His goal was to help the Mages, but after Cassandra points out that he might have made the situation worse because the Templars and Seekers believed the Mages had assassinated Lambert, he admits that it was the wrong thing to do and he regrets it.