I am not against having this option, I upvoted it after all.

But I think 'consistency for the sake of consistency' is a dangerous path.
InDesign’s pages are not Illustrator’s artboards (although artboards can be used as pages).
Artboards are more like viewports, frames that can overlap, nest, easily have various sizes, while in InDesign it takes some effort to introduce a page with custom dimensions. This is the same reason 'layers' and 'artboards' are two parallel structures (unlike frames in Figma).

There is a request about it, BTW:
Artboard-specific Layers — http://illustrator.uservoice.com/forums/333657/suggestions/31133392

So these don’t look like ducks and don’t quack like ducks, therefore no parity — initially. Just a different paradigm.
Still I need an option to keep the zoom level!
And I really want Ai to not zoom into a newly created page as well, like it’s been before it got changed:
https://illustrator.uservoice.com/forums/333657/suggestions/45689917

Indesign keeps the zoom level when navigating to a new page or editing an attribute of a page via the pages panel - why does illustrator act differently? UI parity should be a pursuit of the teams.

K-O, there are users who are completely OK with that auto-zoom approach. Some of them just don’t care, some are really into it.
I’d use both, as I do have different designs. But as I see it, the 'additional zoom to fit' should bee optional, only when I intend to.

The status of it is unknown. 14 votes it currently has usually not enough to push a request above others, with higher vote count... This, again, can signal that not enough of us users care :( We need more attention for it.

What is the status here?

I have never once desired the current action: double-click on artboard in the artboard panel and the screen zooms into that artboard. I have always wanted to maintain my current zoom level. It's jolting and disruptive.

I think its the opposite of the inherent function of that panel.
Think about the typical reasons why a user would be using the artboard panel. They would be managing assets from a birds eye view. Managing being an ongoing process - not ending after you click on one board (initiating the zoom)

Are there any users out there that actually benefit from the current automatic zoom action?

Yes, I need this please. As Helga said, it's a real pain to have to zoom back out every time when there are several artboards to rename. I would be happy with an option to turn the zoom-in OFF in Preferences.

The option to not have Illustrator automatically zoom in on an artboard when moving them around in the panel is critical. You have to constantly manually zoom out to see all the artboards.

As for now, we can use these scripts to jump between artboards with the zoom level kept: https://onthehead.com/#cat-ais-view
I mapped these to Wn + PageUp/Down hotkeys using an external utility, works for me.

I would like it to work in the same manner as InDesign works with pages/spreads. When you navigate between pages (that would be artboards in Illustrator) with shortcuts or mouse buttons, the zoom is maintained. If you double-click on a certain page (artboard) in the panel, it becomes active and Fits in Window.

It would be very helpful to get this option to choose - it's very painful to name & sort a big number of artboards and it keeps zooming into the just named, then having to zoom out again etc.

No.
There should be an OPTION to make it work that way, because some people USE current behaviour.

I would use both, depending on task.
So I vote for this, but only as an option. Not a DEFAULT option.