I'm not really sure what side to take in the question. On one hand, I tend to immediately regret every comment I make, which has led to most of my thought through (if pointless and horribly pretentious) comments being promptly edited into short and vague sentences of praise. On the other hand, I think the transparency of the current system is fundamentally a good thing since it encourages users to somewhat think their posts through, at least those with a predisposition to do so. One might argue, however, that those people probably wouldn't cause a lot of trouble in the first place, and that it's probably too subtle a suggestion for the rest, who likely don't give that much of a damn about what they post regardless.
The only reason I can think of that might warrant the lack a delete function is the possibility of abuse. Shitposting/harrasing and promptly deleting the comments to avoid moderation, or something along those lines. That could be dealt with by saving the comments in some form visible to moderators only, at least for a period of time, though I suppose trolls might still do similar things just for the lulz. Anyway, if the risk of abuse is the reason why the option doesn't exist, then I probably disagree with that. Cunts will be cunts no matter what you do. While there's no reason to arm them, there's not really any way to prevent them, and if there's an overwhelming desire for an option to delete comments among the rest of the userbase, I don't think that risk should be a deciding factor.
I guess there's the matter of preserving comment threads intact for posterity, although I don't see any reason why such consideration should be given to people unrelated to the discussion. It could be worthwhile to preserve the state of comment threads on a website where someone might hope to learn something, but this is a website for Asian comics. The idle curiosity of some voyeur long past the end of a discussion isn't much of an argument. If permanence is the reason, however, the ease and freedom of editing comments completely defeats the purpose of not being able to simply hit delete.
I'm actually kind of curious of why the staff chose to build the system the way it is, and how they motivate that choice. Is there an official statement anywhere? How is it usually done in communities and why? Are there any successful examples (or absolute disasters) to use for reference?
Now, in defense of the status quo, is there really any reason why there should be an option to delete comments? Aside from vanity? A conflict that might stem from a stupid post could just as easily be defused by a humble response as it might be avoided by deleting the offending comment, or in a completely hopeless case, by just ignoring the other person. It's not like you actually need to respond to everyone who bristles at your opinion. Unless you consider wounded pride a compelling reason to waste your time in petty arguments with virtually anonymous strangers. This stance might be a little unrealistic though, I admit, considering the mentality of most people on the internet...
I'm tired as hell and this is too long already so that's enough. I took this way too seriously. None of this should (if it even can) be taken as actual suggestions; after writing this I've come to the conclusion that I don't give a damn. Might as well not post it, but hell, since it's already written... Although I have a sneaking suspicion that I'll wish I could delete this post in the morning.