The important thing to remember is that solid state drives (including USB thumb drives) have a limited number of read / write cycles, so how bad it is for the USB drive really depends on how much the OS thrashes the disk (DSL for example barely touches it if at all - runs all in memory.)
However, you're really just talking in the realms of a slightly reduced lifespan for USB drives heavily used in this way - it's completely safe and won't just kill it. I've used loads like this over the last few years and with the exception of a couple of old ones, they're all still going strong.
It's perfectly safe to run an OS off a USB drive it is also easy to transport with you! But all joking aside it won't really reduce it's life span at all, it might run a bit slower because it's running off USB.