The main exception being cypresses and the like, which, in compensation for their other unpleasant habits, will at least stop growing if pruned at ground level.

I have the stump of a cypress I cut down 10 years ago, which I suspect predated most of the other conifers in the garden, as it was much fatter. All the others I was able to dig out the stump by hand, but this one is too big. But the remaining stump has barely rotted at all in 10 years.

I have rejuvenated overgrown hedges of laurel, beech and viburnum tinus by very radical pruning, ie, removing about 90% of the plant. There's no need to be gentle or careful about it. It is a good idea to make sure that the stump you leave is at least 2 feet below the top of the eventual hedge you desire.