The result is that we saw some ceremonies and procedures that must literally date back centuries.
You are either surprised, or, for whatever reason, feel like stating the bleedin' obvious. The UK is littered with ceremonies and procedures that literally date back centuries. We are big on tradition, and unlike some more "recent" countries, we have quite a bit of history that the traditions have lasted through.
The state opening of parliament, for example, goes back over 500 years. In fact a good chunk of procedures in our parliament date back centuries. And in our courts. We tend to cling on to traditions for state things unless there is an overriding reason to change or even drop them. But if they serve as a flourish to what might be achieved by a far simpler process, but it has history behind it, and everyone has done it before, why change it?
If you want
ancient customs then there is the daily horn-blowing in Ripon, which dates back to the 900s or so. There may be older ones that also,
literally, date back centuries.
I suppose that, to some extent, all funerals are formulaic, but funerals for royalty are especially so. Before mass media, it would have been very important to get the word out to the people about the new monarch, and to parade the previous one's coffin through the streets. These days, I'm not convinced that's all necessary.
The monarchy itself is not
necessary. Every republic and dictatorship has shown that. No tradition is
necessary, I'd argue.
I'm not sure mass media has made it any more or less important to
parade the coffin. People have always wanted to attend in person the funeral of someone they respected. Parading the coffin from church to burial place affords people that opportunity. As does the lying in state before that. Mass media doesn't remove that
want that people might have. So mass media has zip to do with anything, I think. It
does allow people with only a modest interest to watch and be informed.
Is it necessary? No, nothing about a funeral is.
I think that, to some extent, the person the Queen was got somewhat lost in all the pageantry surrounding what the crown means and represents (or has represented in the UK's history).
Well done for stating the obvious again. Or at least obvious to someone in the UK.

There were, and are, and will be for a long time, tributes to the
person the Queen was. TV has been and will be littered with documentaries about this or that, trying to uncover the "real person" and all that gumph. Individuals who attended the ceremonies would also have their memories of the
person, even if it was just as someone who smiled and waved at them back in 1960.
Personally, I am much more affected by learning about the person who died, rather than being asked to respect them merely for the job they held. I think the person is more important.
Then get yourself in front of a TV and gorge yourself on all the repeats of the hundreds of hours of tributes that british TV had over the past 10 or so days. And keep an eye out for all the others that will eventually come out, each trying to look at the Queen (the person) from another angle to any that have gone before.
On the other hand, from the huge public turnout to watch the funeral procession go past, I guess that the British public feels like this is all an appropriate way to mark the Queen's death. People have a right to mourn and remember in the way they feel they need to.
It's the appropriate way to mark the passing of a monarch who has sat on the throne for 70 years, and by all accounts done a fantastic job of not rocking the boat, and actually helping unite. Whether it will be appropriate for future monarchs, time will tell. If Charles III drops dead tomorrow, for example, there'd be something - as tradition likely dictates - but almost certainly not on the same scale.
And it's not just the British public turnout that suggests it is/was appropriate, by the way, but the
4+ billion estimated viewers around the world.
The best part about it all is that one's involvement, for 99.99% of the country (not including children who have to follow their parents), was entirely voluntary. Attend in person... or don't. Watch on tv... or don't. Listen on the radio... or don't.