First off arguing is not allowed probably because it's arguing. Arguing has negative connotations and usually involves some negative confrontation, things we don't want or need on this site. Help Center:
Criticisms which do not add anything constructive ("-1, see previous
comments you scallywag!"); instead, down-vote (and provide or up-vote
a better answer if appropriate); Secondary discussion or debating a
controversial point; please use chat instead;
Second of all, the arguing depending on how heated would fill the comments blocking others and probably lack in usefulness after the first few rounds. Due to the "I said, you said" effect, just useless back and forth.
However, would a discussion be useful? Maybe. I think some discussions are helpful for a site such as this, but the fact that a lot of arguments start from discussions is not encouraging. Or that discussions tend to stray from the point and fill the page.
I think it would be better like mentioned in the comments to link the discussion to the comments or leave them for a short while if it is deemed important and their respectful and not argumentative. However, allowing arguments on other SE's doesn't mean we should allow them. Arguing isn't a positive behaviur and in other sites when it turns really negative and people get banned they get upset. Well, the no arguing rule was made to protect people from themselves. Just because other sites break them doesn't mean we should. This site has other issues beside arguing at the moment, let's not add them please.
But going back to your point, deleted comments do actually hold a lot of info so deleting them sometimes isn't the best action. Maybe having the option to minimize a discussion with a message of why it was minimized would be helpful. But right now that is not possible so going to chat and linking the discussion to comments and maybe the comments for a bit would be helpul.