The problem is that flash-drives are quite limited in speed as compared to spinning hard-drives and SSDs. This is because by their nature, they are not meant for high-performance usage and so use simpler, more basic mechanisms than a comparable SSD or hard-drive (which is also why they are much cheaper).
You can (currently) expect typical read speeds <=20MBps and write speeds <=10MBps. This is usually going to be slow enough that unless you are just using it as a live-OS type of system for data-recovery and such (i.e., occasional, emergency usage), then it will be too frustrating for regular, every day usage.
What is worse, is that by running an OS from a flash-drive, the non-stop writes for logs and temporary files will really eat into the flash-drive’s lifespan. Don’t forget that flash-cells have a limited number of writes before they can no longer be written, and these constant writes will use them up too fast, even with wear-leveling because again, the writes and leveling used in inexpensive flash-drives is not as efficient as with SSDs (which use things like TRIM whereas flash-drives tend not to).
You could run an everyday OS from a flash-drive, but ones that are going to be fast enough will usually also be expensive enough that you may as well just get a cheap SSD and benefit from the enhanced wear-leveling as well.
@DaveM - While speed is one factor, and based on the answers appears to be the most significant one, I was curious about anything on a flash drive impacting OS performance, not just read/write speed. – SaintWacko – 2012-10-04T20:56:30.463