Has anyone been able to find a practical use for live distributions such as Knoppix and Mandriva One?
I tried Knoppix and liked it quite a lot. It was an almost perfect OS, in my opinion. My current PC, however, has a 64-bit processor, and I don't think there's a stable version available yet for 64 bit. But I think there's a typo in your question. Surely you meant to ask if there's anything useful that you cannot do with Knoppix Live. I'm currently using Mandriva, and I dislike it intensely compared with the Knoppix live CD.
I used to use it a lot - but when learning about LInux - Its very good as a desktop OS If you want to play with servers - use Suse Linux Enterprise Server (SLES) or RHES (Red HAT) Knoppix is good for whatever desktop stuff you do
Say you are going to by a used computer, but want to make sure it works, drop in your LiveCD and you're good to go. LiveCD/DVD distos can be sued to rapidly deploy tons of machines that behave the same in emergency situations, e.g. after hurricane disastors last year, emergency centers running LiveCD distros were used to set up Internet stations for people to access email, FEMA and other emergency info.