I've run systems directly from USB (installed there, not live distro) and here's the hiccups I had:

• Slow: USB drives aren't anywhere near as fast as an SSD. Even USB3 drives are far slower than an a SATA SSD. USB3 is 5 Gbps while SATA-III is 6, but the thumb drive controller is often the bottleneck.
• Heat: To get better performance, I bought a higher-end USB flash drive. That increased performance a bit, but the thumb drive ran very hot.
• Durability: USB drives aren't really meant for sustained operation like an SSD. Every time I've tried to run a system full time (granted, that's only been twice), the USB drive eventually crapped out. See also: heat. -Fragile: May not be an issue for a desktop, but with a USB sticking out of a laptop full time, it's going to have very high chances of getting knocked around potentially damaging the drive and/or the USB port.

If the thumb drive is just going to be a temporary / rescue system, that's one thing. I keep several of those in my bag. But for a (semi) permanent install, you'll probably want to have it installed to a real disk.

Edit: I do have some hardware that boots its OS from a flash drive (Ubuquity router for example) but it's configured to not make a lot of writes to it and is mostly read only. So for an embedded system, a USB drive could work fine, but for a general purpose workstation, not so much.