I also want to check those short stories too please share where you read it :3
They are fan fics, not part of the manga - I recall reading this story (I think it was on fanfiction.net or AO3)
The translation in the tankoban is "rip them to pieces" which is actually less interesting, I think. Erase, as you say, could be cut offleave to their fate as he is doing with Sudou. Rip to pieces is an explicit physical threat, so unless he has a very good reason not to go after Sakazaki when the truth about him and Akihito comes out - something like Akihito leaping between them, as he did in Naked Truth with Fei Long, then anything less than killing Sakazaki is going to make Asami look like a man of empty threats. I don't think he will kill Sakazaki, so I'm interested to see how the story handles it.
A while back when we were discussing whether Asami was dragging Aki into the abyss, the idea that Asami may have a code of ethics came up (sorry, I forgot who said it first). Someone had brought up that Asami's group still sold guns and drugs and did things that hurt people, even if we don't see Asami himself get that dirty. This is true, but for some reason I saw Asami as still being more ethical than Sudou or Mikhail (certainly than Sakazaki). By ethical I don't mean nice. I mean playing by agreed upon rules.
Since this is fiction, is it wrong to look for a sense of honor among criminal organizations? Do you think Asami saves Aki just because Asami is into Aki, or do you think that Asami has a code? I think Asami doesn't like to kill unless he is really angry. I think Asami does not like to involve children in his activities. I think Asami finds Sudou's "side activities" distasteful because Asami does have a sort of code--or maybe just an aesthetic, that makes him not want to do certain things.
Do you all think I am over romanticizing Asami, or do you think he's a good man who must rule using dirty tools?