I'm not assuming that, like I said, if they don't invest they are losing money to inflation (which has a historic average of 3%). So the government will drive them to zero either way. Your money needs to grow over time.
I think these examples you gave are definite problems we would have to figure out if we implement something like this. But if France, Italy, and most nordic countries can, we probably can too. I also think its much, much more common for rich people to not pay taxes then I do for the cases you describe (someone overnight owning a 10 million dollar business without time to set up liquid reserves isn't showing up on my facebook feed that often). If we never implement systems because there are possible edge cases we wouldn't have taxes at all :)