Please note that I am talking about my own experiences and I do not speak for the moderator team in this instance.
Dealing with comments is not much fun.
Most of the times the comment flags that come in are obvious and I simply move to delete them. I cannot always check whether they would destroy an argumentative chain or conversation. Comments are not for conversations. In my opinion they aim to improve a post. If that is achieved they can safely be discarded. If they criticise a post in a manner that offers information directly regarding the question, they should probably be answers instead. In all other cases they probably are only tangentially related to the question and should either be deleted after a while or the conversation should have happened in a chat room.
I personally do not like to move comments to chat, especially not, when I see that the discussion is over. Any chain shorter than 20 comments is not worth moving to chat. They will linger there for a time until the chat room itself gets deleted. Why avoid the inevitable.
Selecting comments is a no go for me. Either the conversation should be moved in its entirety or not at all. The process of anything else would be tedious and I cannot even start to imagine the pain I will have if I do something one of the participants is unhappy with. I have been 'shouted' at for less in the past.
In my personal opinion: Every comment should be deleted; if it were important enough to be kept it should be an answer or directly incorporated into one. I'm sorry if this sounds harsh, but one of the reasons I like this platform is that I do not have to read through conversations.
Some more clarifications:
Some comments are just comments, not conversation, being trapped within conversation of others. I agree comments should be eventually deleted, but probably not before their reason is addressed. It may be minutes and it may be years. Some comments do not have much sense as an answer or are not suitable as an answer due the complete answer policy.
If you find a comment missing (because it was moved to chat or deleted otherwise), please raise a custom flag and the moderator team may restore such important ones with critical information.
If there are comments to my answer, I usually include my response to the answer, but it is mostly not applicable. I remember as the 1st comment laconic note from Ivan Neretin "No, it is not" but was moved to chat as extensive discussion. Quite funny.
I am sorry, but I do not get it. Neither the reference, nor why it would be funny.
As I said before as a moderator you'll have a choice: all or nothing, or quite a bit of extra work. I am not going to do that extra work for some random discussion. If some other people decide to use the comments as a chatterbox, then that first comment will be moved, too. There is no selective moving.
Just to make you aware of this awful process: Selective move would mean deleting the comments not belonging to that conversation, then moving the conversation to chat (which by the way can be done exactly once), then undeleting the comments which may still be relevant. Given that you are dealing with extensive discussions that means reading the whole thing again, and again, separating out the ones that have been deleted from other reasons.
I am thankful for you including remarks into the answer; this is not the standard.
If there are comments of just 2 users, than usually is soon raised the trigger to be moved to chat, what I often use. And there is still selective option to post a standalone comment as usually, out of the chat.
If that automatic link is triggered then usually some kind of conversation is happening. If you want to discuss an answer or question, you should do it in chat. You are a high-reputation user, you can create these rooms before that automatisms trigger, or just use the periodic table. There'S not much going on currently.
But if multiple users are involved, in my experience such triggering to move to chat does not happen, or at least the mod intervention comes sooner.
The automatic 'move conversation to chat link' only picks up a conversation between two people.
The automatic system flag only triggers by itself if there are more than 20 comments. Othertimes a user raises a custom flag. In both cases it is at the discretion of a moderator to move comments to a chat room. I usually don't do that, because I see no point in creating chat rooms that no-one will visit.
There is only intervention by one of the moderators if there is a reason to act. I personally would never proactively move comments to a chat room.
As I said before it is no fun.
Further clarifications:
I agree with the general policy of moving comments with extensive discussions to chat.
There is no such policy. This is a service moderators may provide If a conversation is still ongoing and/or worth retaining.
But, I have frequent feeling this mod feature may be occasionally used too aggressively.
I really wanted to avoid talking about it, I really wanted to let this slide, but I am offended by this. There is nothing aggressive about moving comments to a chat room, it is the opposite. I might have agreed to a certain degree if you had claimed that the moderators would be purging comments on a regular basis; of course that is not true either.
You might not have meant it that way, but to me it feels like you are accusing the moderator team (which includes me) of abusing site mechanisms.
I would be interested to know the community opinion how to deal with "seeds and weeds",what mods can and cannot do and what would be eventually too much effort for them. And what common users can do to help mods to eventually keep useful comments and move the rest.
I cannot speak for the community, I cannot speak for the moderating team; I can only speak for myself. If you are forced to read a block of comments, then understand the answer and the questions they belong to, then judge whether any rules are broken, then decide whose feelings get hurt when you delete one too many comments, then get accused of doing just that thing, then well, that is too much effort.
It takes a single flag by one of the users to create an avalanche of things to take care of, because one of the other users did not agree and has no knowledge of the flag.
Also I think with 'what mods can and cannot do' you mean what you want the moderators to do, which rules you would like to set them to follow. Or do I see that wrong?
Personally, I frequently delete my older comments, that look in hindsight like little "chatty", from the comment chain. But without all participants doing so, it may not bring much gain.
If you are deleting your old comments, then please flag the other ones for removal, too. Nobody needs half a conversation.
This has become a rant. I'm sure your intentions are nice, but without more data, it is hard to not take this general post personal.
I reiterate: Everything I have written here is my personal opinion.