I remember it all too well for various reasons. But I never "got it" either.
I was away with friends at the time, and they all fell into wailing and gnashing of teeth style grief - beyond me. I was embarrassed for them. We had to come home the day after it happened, and they were still going on.
My mother was in ICU at the time (she had TOLD me to go away as she would be fine - she was) so she was more of a worry than Lady Di being killed in an RTA, tragic though that was in general terms of a 36yo mother being killed.
What REALLY drove me nuts though was the radio. I had to switch if off completely for a week, because they kept going on and on and on and ON about it, and playing that bastardisation of Candle in the Wind (which I used to quite like).
I worked the day of the funeral, with my 2 line managers. We were all of the same opinion and couldn't think of anything worse than watching it. Several of our colleagues were grateful to us for taking the duty though, so that they could watch it.
I never had any time for her back then; I thought she was manipulative and wasn't at all keen on her.
But what I have found, to my own interest and mild dismay, is that in watching the 20 years later shows, I'm feeling more sympathy for her! I don't know if that's because I'm now a mother myself or just because age brings more empathy (sometimes) - but I'm definitely not as hardline against her now as I used to be.
And yes, I watched the 20 years later show in Australia - I know they like to think they'd rather be a Republic, but for all that they show a remarkable level of interest in the Royals still, especially Diana and her sons.