It should indeed be a standard feature, especially for expensive headphones. I mean, look at the Beyerdynamic T5p for instance. It's one of the most expensive "portable" headphones around and it has such thin non-removable cables. This alone is enough reason for me not to buy them. Not gonna want to send my expensive headphones away just because I accidently damaged the cable. And why doesn't the T1 have removable cables? It's nuts. I guess they want to keep production costs as low as possible.
It does also depend on the construction of the cables.
I know of extremely thin cable that is absolutely unbreakable.
If you mix Kevlar in with the copper you can have a very very tough cable - especially if there is more Kevlar than copper.
Sennheiser do an extremely thin, just 1mm in diameter, cable for their tiny tie microphone for stage use. There was a story (and I saw the pictures) of a case where a microphone cable caught in the costume of another actor on stage. It was so bad that it completely ripped the plastic outer sheath of the cable and left it flapping - BUT - the cable itself did not break and the microphone continued to work perfectly!