A lot of Charles’ ‘busy-ness’ in the immediate aftermath of QEII death reflected the need to show continuity of the monarch; “the Queen is dead, long live the King”. The last time that happened TVs were still relatively uncommon, so it was mostly radio and cinema newsreels. There was still a need for physical visibility in various places in a way media and internet make more unnecessary these days. People enjoy a bit of historic spectacle too and something had to fill the week of mourning.
I suspect when KC dies his death will be marked in a much more restrained way - there just isn’t the same attachment for him, partly due to the much shorter time he will reign.