You've pretty much summed up why billionaires shouldn't exist: their existence is incompatible with democracy. (I don't know how best to fix this either.)
It's telling that the responses to a non-serious tax plan are not on the topic "why billionaires existing is inherently good" but like this where you argue that billionaires have too much control over the democratic process for it to be implemented and a concern over the administration of a small scale sticker run.
Consider for a moment what privileges would have to attach to this sticker, in order for the billionaires to let this through Congress. Definitely they would still want to have control of dominant cultural narratives, and they'd still want to write all the laws, and those of them who appreciate fabulous personal possessions would still appreciate those. The administration of this sticker would be quite complicated...