Concerning easy-outs:
If you have exactly the right size easy-out and the metal of the easy-out is significantly stronger than the screw (i.e. it’s not a crappy Horrible Freight one being used on a hardened bolt) and you carefully drive it a little ways into the target hole, but not so much that it bites through to the threads, they work great. Lotta caveats here, including a requirement for what Pirsig called “mechanic’s feel.”
If you bust off an easy-out, you will discover that the metal of the easy-out is nearly impossible to drill; I can do it with a drill press but I only know one person who can do it by hand (and he can torch out bolts, too, so we’re dealing with extremes of hand-eye co-ordination not reachable by the common man). The drill bit will want to skitter off the shear surface of the hardened easy-out and bite into the surrounding metal or possibly your hand. If you press too hard the bit will bend and skitter anyway, or else snap off and embed itself into your safety glasses.
If you have a situation like @anon27554371 where the bolt’s already got a stripped allen hole, knocking on the right size easy-out until you get a good bite and then turning with a small crescent wrench will usually work. You’ll need a quality easy-out, though, and if you bang on it too hard you’re likely to find out that your threads are brass or pot-metal, and as @wrecksdart says the hole has to be deep enough that the easy-out does not strike bottom. I usually try to find a slightly larger allen (a metric one for an SAE allen, or vice versa) and knock that in with a small hammer before I resort to an easy-out. And I’d never use an easy-out on anything that I could get a vise-grip on.
Pirsig talks about all this on P250 of Zen and the Art of Motorcyle Maintenance, I think.