In physics there are events that happen that are very random from any point of view until after they have happened. One type of example is nuclear decays that cause radioactivity.
As I just wrote,
<<<Yes, I was discussing that in an earlier post. One thing that I disagree with is the notion that after they have happened, they don't appear random. Where does that come from? If it's random then it's random and randomness is all about appearance because appearance governs predictability.>>>
A random event is random after it happened because it's part of a random sequence.

@elroch, I appologzie if my opening post appear convoluted to you.
Are you sure I said that? I can't see why I would have.
however, since your idea of true randomness largely contrast mine, I must ask you to align with the topic.
Actually, you brought up the specific point I have focussed on. See below.
thank you in advance for your corporation and contribution.
You're welcome!
It's worth noting that the discussion of a form of randomness in physics that definitely cannot ever go away is an answer to the point you made in your opening post when you said:
"4. Randomness is a reflection of our ignorance about the thing being observed
rather than something inherent to it."
It is this hypothesis which is not true for the quantum systems considered. The randomness is definitely inherent rather than being just a matter of us not being aware of some hidden information. Your thinking has a long pedigree: it is close to what Einstein hypothesised, but which was eventually proven wrong.