Dumbledore died because he made a mistake. the injury to his hand was cursed and Snape was only able to contain the damage as a temporary measure.

I think the lesson is - that - no matter how brilliant we are - all of us are capable of making mistakes and all of us will die at some point. Mortality will befall anyone. People die every day and the impact of their loss will forever affect us.

There is never a 'good time' for someone to die - in terms of convenience to others around you.

to quote another wizard in another series.
'all we have to decide is what to do with the time that is given us'

I believe the 'lesson' of death, is to remind those of us who live to appreciate the time we have, and to make the most of our time on earth.
Having lost people, I think, this is what JKR wanted to address.

People die - young, old, sick, healthy, by accident, by murder....

and yes - it isn't fair. But it never is. It never is.
Perhaps you are fortunate enough to not have lost someone close to you.
or to see someone so sick that it is only months left that they will be alive.

sorry for the rambling - I've been wanting to try to answer your 'what was the point of dumbledore dying' question for some times.