… My experience with other websites in the Stack Exchange network is very different …
… and if for instance I go to the top answer at the top StackOverflow question, I see there are 64 comments on that answer.
StackOverflow is one of the many sites of the StackExchange network. All sites work according to their own rules!
Meaning: what may be on-topic at one site, may very well be off-topic at another. This – among other things – becomes apparent when you check the individual help centers and individual close reasons each site provides and uses.
So I wouldn't say 5-10 comments is necessarily "too much noise".
Generally, that number indeed doesn’t sound like much noise. Yet, it should also be noted that after 5 comments, all following comments are hidden behind a system message… therefore it sometimes sure makes sense to separate the noise from the usable comments.
Now, let’s look at what exactly was moved to chat (and not simply deleted forever):

The question is rather broad, and more than a truckload of answers are possible.
- fgrieu hints at a potential answer
- OP clarifies he/she is already aware of that one (somewhat voiding the need for above comment)
- fgrieu therefore hints at another potential answer (was later merged into comment 1)
- Biv asks if his potential answer would qualify
- OP confirms that
- Biv states he’ll post an according answer as soon as he can
- OP says thanks (this somewhat voids 4-7)
- squeamish posts a potential answer
- YOU post a line about your personal opinion related to Shor et al.
In the end this boils down to some back-and-forth, and some hints at potential answers which might or might not be interpreted as clarification attempts…
Problem is: the commented question itself is rather broad and a bit unclear when it comes to what is being asked (we have a pretty alike Q already – dupe?) and therefore it opens the doors to a truckload of short comments/hints. Actually, due to the broadness of this particular Q, the hints in the comments practically transformed into "potential answers" and could actually have been posted as answers as well… as said: in this particular case.
Other questions are different, and there it makes more sense to leave hints as-is. In this particular case, it made more sense to wrap up the comments in a community wiki answer – which MaartenBodewes created and I added the commented hints into, putting the usuable hints/comments in focus.

Long story short: in this particular case the noise was moved to chat, while the hints were merged into the community wiki answer. Nothing was deleted.
The extended notice I added to the "comments were moved to chat" link (not visible in above screenshot) was merely a general reminder; like a heads-up. Nothing more, nothing less. It was not meant to target any specific user or comment, but more of a "just be sure to remember…" as some comments to that particular Q quickly rendered themselves "obsolete"while others started bordering "too chatty".
Fun Fact Aside
A few hours later, the OP of that question edited his Q to clarify his/her "research efforts" by listing all hints at potential answers which were mentioned in the comments and (in consequence) the created community wiki answer.
That edit by OP practically voids all comments and even the current version of the wiki answer. (Expanding the answer by adding to it will solve the later.)
Not judging if OP’s edit really is the result of research efforts or not, the problem of the Q being a rather broad and somewhat unclear question remains. Neither of the provided comments, nor of my "keeping it clean" efforts, nor the edit by OP (which curiously lists all commented hints 1-to-1) could change that
Hints or pointers are welcome nevertheless!
Generally, providing hints or short pointers as a "heads-up" in comments surely tends to be welcome (just think of all the helpfull hints when homework-alike Qs are posted) – which is why we moderators tend to leave most comments alone. We only clean up stuff or enhance things when it makes sense. For example: if comments resolved something and thereby rendered themselves "obsolete", or if they mutated in a "too chatty" back-and-forth.
The reason to sometimes "clean up" some comments is pretty simple: sometimes, "comments aside" tend to hide very usefull hints and information between some chit-chat. When that happens, it definitely makes sense to move some stuff to chat… as that puts the usefull hints and informational comments back into the focus they deserve. Let’s be honest – no one will scroll through 10+ comments just to see if there’s a valuable hint hidden between some noise… where "noise" can be anything ranging from "funny note aside" to "full discussions". The means chosen to optimize comments in such cases can be very different: "move to chat", merge two or more comments by same user into one comment", etc. If comments are cleaned/optimized, the goal is to put focus back on what is being asked as well as all the valuable information posted as comment and/or answer. Sometimes flags point us moderators to such things, sometimes we happen to stumble upon such situations ourselves. If it makes sense, we try to make things better.
About posting answers as commments
Having said all the above, there’s this fine line between "a hint" and "an answer" we haven’t talked about yet.
See, we frequently have situations where someone asks something, a comment answers what is being asked and OP is happy enough to abandon the Q. Most of the time, such Qs end up "unanswered" from the SE system point of view. That’s something to keep in mind, the reason why I added the heads-up notice to the chat link, and something we all need to watch out for. Good SE sites have questions with (accepted) answers, not comment-answers.
Related to this, we happen to have a META question which I personally asked some years ago while I was still a regular user; so before I became a moderator at Crypto.SE:
Looking at what StackOverflow META says about comments
Actually, there’s a pretty good Meta Q&A about comments at StackOverflow:
Excerpt:
When should comments be deleted?
Comments are temporary "Post-It" notes left on a question or answer. You should not expect them to be around forever: Once a clarification has been made, an edit added to the post to include new information, or the issue in the comment is otherwise resolved, it is subject to deletion. In reality, many obsolete or chatty comments remain untouched due to the high volume of comments posted, but this does not mean that they can't or shouldn't be deleted in the future.
Looking at what the Crypto.SE system says about comments
Last but not least, I’ll simply post a screenshot of the placeholder text as both a heads-up, as well as an additional indicator of what SE thinks about how users should be using comments:

I think that somewhat wraps things up.
TL;DR
Always feel invited to use comments to ask for clarification, to hint at something, or to give a heads-up. Yet, always ask yourself it what you’re posting isn’t actually an answer. If, please consider about posting it as such. You might even gain some reputation points when you do.