I guess every person's experience affects them differently in that regard mate. I appreciate that you recognise that 'it's just you' (it isn't - many would feel the same).
As I revealed last year, I have a connection to a family friend of the Dorsett's, so I can't say anything objectively here - but in terms of other events, some people see their own friends or family in the faces of the victims. Simply having a child \ relative who is the same age\gender as a victim or relative of the victim.
A parent with a 12 year old daughter would easily be horrified to think of this situation, as the little girl Ebony was 12 at the time - and their thoughts would turn to "what if it was me?" (And likewise baby Evie - only 8 months old at the time would impact anyone with a ~1 year old). Many parents with similar family arrangements would fear this, and grieve for those they didn't know - laying flowers or paying respects in some way would perhaps give them some comfort, as it would be something they would like to happen if it happened to them?
Sure, there are those that would rhapsodise about how badly this event has impacted them despite no connection or link (an 18 year old boy without kids would likely not have much in common with the event to be impacted), and would crap on about it in forums or social media as a form of attention seeking 'woe is me' approach, but i think in general, those who do it quietly, respectfully, without publishing how "hard" it is for THEM on social media, who quietly purchase a bouquet or tribute to lay at the grounds before heading home deserve the opportunity to deal with the events in their own way.
Agree with you on the 'small memorial, 5 minute media call, quick safety message, and drop it for good (publicly)' is probably the best course for them though.