The Timeline can get very busy and important Activities, like event bookings, DBS checks,etc can get a bit lost.
What would be useful would be a tile on the Constituent Profile which displayed a short list (5?) of 'high priority' activities. This could be controlled by either adding a 'display on profile' tickbox to Activities in the Configuration, or directly on a specific Activity in the Timeline, similar to the 'Show as Alert' tickbox.
I think this might also be an alternative to my other suggestion about adding Custom fields to Constituent records. You could instead have a 'Constituent Details' activity with custom fields defined and have this show on the Profile. A lot easier to implement, I'd imagine.