I thought they might be spring steel so they can flex.
Not with a pivoting external extractor like most modern guns. They are designed to pivot outwards as the ejector hits the case to allow the rim to slip out. They are usually of fairly thick crossection too. Much too thick to bend with the forces involved.
At the very least, they will need to be harder than the material they are moving against.
Most of them are probably not through hardened just surface hardened leaving a tougher ductile core, but since they usually have very sharp edges, the edges are going to be through hardened just because they are so small in cross section. Hard materials don't like shock. Sharp corners also result in stress risers which can concentrate stress in a very small area causing a fracture. Snapping over the rim repeatedly can cause shock that it wasn't designed to handle.
It might very well go for 1000's of rounds without a problem then chip the extractor and the gun starts losing control of the fired case.
Some guns have very beefy extractors (without extremely sharp edges) that are designed to do this. (Shotguns, apparently the Beretta 92, push feed bolt actions)