There are Easi-Outs and proper extractors!
The conical left hand thread, uber hard, screw in until it (usually) breaks breed are indeed a monument to the creativity of Beezlbub and his minions in devising ways to frustrate humanity.
The drive in splined shaft variety on the other hand do generally work as the hole is sized so that the splines displace material from the seized bolt around the main shaft to give the tool something to grip on rather than expanding the remains of the broken bolt more tightly into the threaded hole. Basically the professional, sorted, version of batter in a Torx bit, cut off allen key, file tang or whatever is this weeks favourite thing with sharp edges.
I got Numbers 1 to 5 of the original breed made by Ridgid tools from the Snap On man longer ago than I care to admit. Very much not cheap then but effective. See **LINK** for the current UK source. The basic extractor sets sans drills, guides and snazzy box are, I think, quite affordable. Its nice that you can buy them individually should you break one. I'm on my third No 1 (the teeny one) and second No 2.
These days Snap-On sell their own BluePoint brand sets, even more not cheap, and there are various less expensive knock-offs. Some no-name imports, probably of "are you feeling lucky" quality judging by the price, others from respected brands such as Sykes Pickavant. I'm periodically tempted to get the cheapest set I can find for the box, drills and guides but having managed just fine without box, guides or dedicated drills for "mumble-mumble" years splashing out on extractor numbers 6, 7 and (maybe) 8 is more likely. No 8 is serious money but it is a big brute needing a 16 mm Ø hole. If you need the No 8 you are likely snorkel deep in the kitty litter!
Clive