Why should you be allowed to edit recorded history so that you have always thought what you think now?

Because it is a reality of human psychology that people will status-penalize your current self for the mistakes of your past self, even if they (say that they) try not to.

That may be a general problem, but on Less Wrong, what I typically observe is that people get upvoted for accepting counter arguments and changing their mind and for apologizing for rude behavior. Sometimes downvotes are even removed from the rude comment that required the apology.

Also, it would be undesirable to have a bunch of new comments of the form "I've changed my mind about that semicolon". Such comments might even be downvoted, resulting in a no-win situation for the commenter.

As I have said, that is a fair use of the edit feature. But it is not the use that you were defending.

And you're not actually editing recorded history.

That seems to me to deny basic facts. The comments are a record of a discussion, editing them to say something different destroys that record.

People know the rules, and know that comments can be edited, so expect that people will try if possible to make all their comments make their current self look good.

The fact that people know the rules, and do their best within those rules, does not mean there are not better rules that allow people to generally do better.

It would furthermore be unfair to freeze edits without also freezing voting.

Why should those issues be linked?

To prevent a situation where someone is hemorrhaging karma and unable to do anything about it.

People who generally write high quality comments are not going to hemorrhage enough karma from their momentary mistakes to put them under any thresholds. Once you are above 20, additional karma is just license to screw up.

In general, this a case of "leave well enough alone", or, "if it ain't broke, don't fix it". Editing comments -- like any feature -- has potential for abuse, but it's not currently causing any problems severe enough to outweigh the benefits.

It doesn't happen very often, but it is quite irksome when someone edits their comment so my reply doesn't make sense. (And it tends to happen more often in more heated discussions.) I expect this to happen more often as Less Wrong attracts more members and the level of the median member goes down, even as the level of individual members goes up over time after they join.