With all due respects Bill, slates really are tougher than you seem to think, and it's perfectly possible to 'lift' these without damage as they are not fitted that "tight" (and that includes Welsh, Belgian, Asbestos Cement and today's Asbestos-free ones) by using the proper tool for the job - a slate ripper. The problem is actually re-nailing the last slate in a repair below the ridge line because the nail would be covered by the slate above it - and this is where lead or zinc 'tingles' are used at the bottom of that slate to stop it falling. [1]
When you see slates broken the way that you describe, this is usually caused (apart from weather) by the uninitiated/dim-witted and cowboy builders trying to lift the slate using screwdrivers or any other odd tool that comes to hand.
Tiles are an entirely different kettle of fish to fix.
[1] I've even seen the 'new-fangled' silicone mastic used to 'stick' slates in place by the unscrupulous from the first time the stuff came into general use on buildings.Cash