It depens, for very hoped beers and especiall for beers wih a high amount of late hops it is important to both remove the hops fast after flame out AND to cool it repadily down under 80´C. Else you will still have an isomerization of the bitter part of the hops and hence a more bitter beer. If you have only used hops at the begiining of the boil or a low IBU beer I don´t go to exstremes for cooling it down fast.
So in all, for high hops beers with late additions, I would reccomend to both remove as much of the hop material either use hop-bag or pour though a stainer, and sametime cool the wort down as fast as possbile either activily or cool pot with Water/ice in sink! I have also added cold water directly to the hot wort to cool it fast. Some questions this approach couse to oxidization.
It should be noted Beersmith2 can calculate taking the time it takes to get Down under 80´C into account, e.g. hence take the isomerization into account under cooldown!
So I use the easy chillling where I let the wort cool Downs by itself over the night, but for beers with late additions of hops I take action on as fast as possible to get it below 80´C. I capture this time and use Beersmih2 to calculate this impact on IBU then!