They have been known to burst, even thick as they are.
I invested in a set for my washer. That said, I hardly ever see the braided variety on people's washing machines... everyone I know uses the ones like you have, and I've never personally known anyone that had them burst.
It's not so much the chances with me as it is what's at stake. It can cause enormous damage to your house if they break because the lines are big enough to deliver a huge amount of water. To me, the $20 a set costs is worth the peace of mind, or.
At the very least, one should always remember to shut off the valves in the valve box before going on vacation.
The other thing that's bad are those plastic flexible hoses that connect between the shutoff valve and your sinks/toilets. My sister had one go in her place and had to have all her hardwoods redone and a lot of carpeting replaced. We had one go at work and it flooded our entire warehouse. They make braided steel covered hoses for these too.