Depending on how one reads your post, it can be considered as two or three (or perhaps even more) closely related questions.
- Could (and should) we change behavior of the community user such that it bumps questions which have no answers? What are the reasons why this feature request currently works the way it does?
It seems that the main purpose of this feature is not to bring unanswered questions to the attention of users. It is about bringing attention to answers. I will quote from this post: How can we make the purpose of Community "bumping" more obvious?
To be clear, the intent here is to resurface questions that someone has attempted to answer, but which haven't yet attracted any votes to either confirm the usefulness or decry the worthlessness of the answer(s) that've been posted.
So changing this to bumping questions without answers would mean using this feature for a different purpose than originally intended.
As with any automated system, it is probably difficult to define good criteria how to choose questions which should be bumped. (I.e., questions where additional attention might be useful.) I do not know whether all details how community user selects the questions are publicly known, the algorithm might be quite complicated. For example, only recently I learned that number of views is also taken into account.
- Is my understanding that community user does not bump questions with no answers correct?
I wrote questions with no answers rather than unanswered questions since by the meaning commonly used here on Stack Exchange network, the term unanswered question includes question having an answer, which is neither upvoted nor accepted.
After this modification, the answer to your question is: Yes.
Some links to the basic info about community user can be found in the tag-wiki. In particular, this post contains many details about what community user does: Who is the Community user?
Specifically to your question this meta.SO post seems to be relevant: Community user does not bump questions that never had an answer I will point out that it is tagged as status-bydesign.
- Are older questions with no answer doomed?
The exact quote from your post is:
So if I understand correctly, a question with no answer at all is consigned to oblivion if there are no answers or edits.
In my opinion, the answer to this is certainly No. (Although the likelihood to getting an answer is definitely much smaller.)
Bump by community user is not the only way how a question can be bumped.
Already in the answer you linked, apart from editing also bounty is mentioned as a possibility.
And even if an old question is not bumped and does not get to the front page, it is not the only way it can get to attention of potential answerers.
- Already here on MO there are many ways in which the users can get to that question. The list of the most recently asked or most recently modified question are not the only things which the users see. There are many other places where the question is listed. Perhaps some users browse through unanswered questions to find some interesting gems or even simple questions which, for some reason, lack answers. There might be some users who occasionally browse through questions with tumbleweed badge, to find questions which did not receive much attention and to see whether they are able to help with some of them. Somebody might spot the old question among favorites of some user or in the sidebar among related questions to some recent question. Some users even have collected in their profiles links of some stuff on MO which they consider interesting. Somebody can get to an old question because it pops out when they are searching for posts about some topic they are interested in. And there are many other places where the question might appear. (Admittedly, the number of views will increase more rapidly after the question has been bumped, but it will probably continue to grow even without bumping. By randomly browsing questions with popular tag badge, you might get a rough idea how long it took those questions from posting until gaining 1k views. Some statistics about how soon after a question is asked it gets answer can be found using SEDE. I will mention this post on meta.math.SE, the query provided there can also be used for MathOverflow. However, the detailed analysis would require more work. Since this is not exactly main focus of this question, let's leave it for another time - or for a user who is interested enough to do the work now.)
- It is possible to bring attention to a question by mentioning it in chat. (At the moment the main chatroom seems to be almost unused, so that would probably not generate too many new views. But it is possible that this might change in the future. However, there is a very active room focused on homotopy theory, so for inquiries from this area chat is a good option. And maybe in the future some other rooms will be created and become active. I will also mention that math.SE has several chat rooms. The main room is very active, other rooms less so, but some of them had periods of rather big activity in the past. If you decide to post something there, it might be reasonable to read rules of the room first.)
- There are even some rather bizarre ways how the question can get renewed attention. They happen probably rather rarely, but they do happen. For example, your question might be used in review audit. (Although that gives only one additional view by the reviewer, unless they decide to edit or answer the question.) Or the question might be bumped because a spammer post an answer advertising some product. (Spam occasionally appear here - some rough stats were mentioned here.) However spam is probably more frequently posted as questions rather than answers.
- And there are certainly many ways how somebody can get to the question from outside MO. For example, it might be mentioned on some blog or website. Questions from MO definitely appear on social media like Facebook and Twitter. (For example, this Google search returns several MO question posted on twitter. And I am pretty sure that many more MO-related tweets than the few results found by this simple search exist.) Or it can be discussed even in email exchange or discussion over lunch with a colleague.
- And probably one of the most frequent ways is that somebody gets to some question is finding it using Google (or other search engine). The users with 25k+ reputation can see in site analytics what are the most frequent sources of traffic no MO. But even without access to site analytics it is easy to see that MO questions typically rank high among result of google searches.