Scrum's view on the Daily and on Management
The 2020 version of the Scrum Guide says this about the Daily Scrum artifact:
The purpose of the Daily Scrum is to inspect progress toward the
Sprint Goal and adapt the Sprint Backlog as necessary, adjusting the
upcoming planned work.
The Developers can select whatever structure and techniques they want,
as long as their Daily Scrum focuses on progress toward the Sprint
Goal and produces an actionable plan for the next day of work. This
creates focus and improves self-management.
Nowhere does it say anything about how to achieve those goals, whether it's push or pull or whatever other dialog structure, nor does it forbid any particular technique.
Nor does the Guide say that the main purposes of the Daily is collaboration! Collaboration is of course a tool to solve problems and to work on things where collaboration makes sense, and also inevitable given that all members of the Daily are on the same power level, and an inherent part of everybody informing everybody else. But as written in the Guide, the purpose of the Daily clearly is inspecting progress (and fixing problems that come to light during this inspection).
It says the following regarding management:
If the Product Owner or Scrum Master are actively working on items in
the Sprint Backlog, they participate as Developers.
This means that aside from the devs, only the PO or SM are there, and only if they have an active role in the sprint backlog, so they are there in the role of a developer, not SM or PO. So this clears up one part of your question: the role of management is clearly not here. There can be no "status pull" if there's no management to pull, unless you are of the utmost pessimistic opinion that the team informing itself about its own status is already a negative thing.
Fixed dialog structure
The three topics "what have I done, what will I do, and what are my impediments" do not need to be so utterly destructive as written in many of the other answers.
They are a guideline, a framework, especially if working in a team where the dailies are not yet the grandest event ever. There are still worse kinds of dailies than this (for example, by the PO taking the time to babble on and on about whatever they need right now...).
Also, they solve the "blank paper" issue. Not every developer is a great rhetorician, and in my experience it is noticeably freeing in such meetings to give a common structure, so everybody can remember. This is similar as in other dialog formats (for example a "round table" where each person is explicitly called up to say his opinion on a topic by a neutral moderator). Sure, many people scoff at structuring dialog, and every kind of structure is viewed as oppressive, but there is a reason they exist, and when one gets a bit over the weird situation, it can be very productive.
In fresh teams, where everybody is already used to Scrum in general, having such a common ritualistic structure makes the process of getting to run well together very smooth. Even the most fresh dev, who maybe does not even know that he has a problem, yet, can say what they are doing and what they are going to do; and if there is the common problem that they simply do not have enough information to pick a new story (or how to do the current one in a good way) the team can immediately chime in and offer help, pairing sessions etc.
Also, nobody said that this must take long, be boring, or that there should be a lot of focus on the "what have I done" or "what will I do". Of course most time should be spent with the impediments, and often collaboration is the cure. These three formulaic questions are just the triggers to get the discussion started.
Finally, not in every team every person is checking the sprint backlog or board religiously for individual changes. Sometimes it's just nice for the team to update itself on who does what, especially in a remote setting. Some answer said "it's useless because everybody knows what everybody is doing anyway", but my response to that would be - if they knew already, they spent time on finding that out. They can save that time because they will be told in the standup. Zero net change.
The time wasted can be absolutely minimal if nothing of import happens. In my dailies, on good days (i.e. no impediments) it's over in a few seconds per dev. "What have I done" and "what will I do" can literally be a half-sentence each. We even allow for "I have just finished on XYZ and will pick one of the open stories next"; this (the second part) is valuable because at this point a team member can chime in, ask for help, seeing as the dev is free currently, or point out ideas about which next story would be most important etc.. But I would be worried if someone said "I have worked on my last story and will work on my next story" - that is a clear sign that something is going wrong - that dev is simply skipping his part; and if they can't even tell us what they have been doing up to right now, there is a high likelihood that they also would not tell us what their current impediments are.