The most important factor for mainspring is, as far as I understand the matter, is their yield point.
In this regard, Kevlar beats steel by at least factor of two. So why aren't we using it instead of steel in watches, well their mainsprings specifically.
I could understand the costs factor, but even premium watches seem to avoid it. As a matter of fact, finding any non-steel mainspring is pretty rare.
Is there any reason for that?