Glad it worked.

I understand the frustration.
But it’s fair nonetheless. While it seems like an extra step, it’s not. 'Expanding a shape' means only converting it into a path — with no modifications like removing handles. Basically Ai just drops the stored definition of it being live, rip offs the label.
And handles are most probably required to avoid having the widgets drawn for each new point and keep them drawn only for rays.
Ai has to keep them, because otherwise it won’t be able to convert the resulting path into the same live shape, if one chooses. If you try to convert a path with reduced handles (using the Simplify method) into a live shape, Ai will do it wrong, seeing twice as many sides and no corners at all...
Not sure if this can be easily fixed.

To the second part — when I try to call Object > Expand for a live shape (being it a star, or a rectangle, or an ellipse), the dialog appears for me... but the 'Object' option is disabled. I personally think that Ai should allow to this common expand dialog for expanding live shapes, but never cared enough to make it a request. But you say it just doesn’t pop at all?

Thanks Egor for the reply.

I see your steps and they do work.
It's just that the extra step was never necessary. Expanding the shape meant "expanding" or "baked" or "flattened." So to me, this is a bug. Also, when I did go to "Object > Expand...," no dialogue box appeared either.

Otherwise, thanks for the solution. I do hope that there can be a quicker solution in future updates.

Have a great day.

Lourens, this is interesting.

I was able to reproduce what you see, and this is what’s happening.
When a star gets expanded, the inner points of it have handles, even though the segments are straight (take a look at the screenshot attached).
Since Illustrator does not STORE the data on corners, but RECOGNZES them in any given path, this combination of handles FORCES it to see original corners you made when modifying a live star. So Ai converts the live star into a just path in a CONSISTENT manner (which is fair!)

But now to make it show corners widgets for the actual corners, you can remove the handles (exactly what you did manually).
There is a faster way to do it!
Call Object > Path > Simplify, and click the 'cog' button, to open advanced settings.
Enable 'Convert to Straight Lines' option and reduce the threshold to zero (just like the second screenshot shows).
This will force Ai to remove all the handles without removing any points.
Press OK and there you have it — all corner widgets are there for all the points.

Does it work for you?