it also would serve no real purpose;
The randomly assigned people would just become the new plutarchs overnight. The problem is the gross difference between incomes among the populace, not who is currently wealthy and who is not.
Personally, I think it would be better to impose increasingly burdensome bads on people who fixate on being the wealthiest of the wealthy instead. Taxes have been a historically tried one (that gets loopholed to death). I would suggest something more constructive though.
The major quasi-religious petard I keep hearing is that "private interests" can do a better job with helping the poor and all that, so we should codify into law that they are responsible for that, with the degree of responsibility heaped on them being consistent with the curve distribution of their wealth. EG, people in the top 1% are legally responsible for the healthcare and welfare of the bottom 99%, with the top earners being responsible for the greater portion of that assistance. They can render that assistance directly if they want (such as via a charity, or even writing checks for medical care for poor people) but they have to keep reciepts, and must provide that proof at the end of each year; The goal being that all that capital gain and wealth increase they are engaging in must also reimburse the society for its extraction from society, with the goal of harnessing that drive to improve standards of living across the whole of society, and not just in the top 1%.
It's a silly idea sure-- but I think it might be interesting to try. Throw in actual penalties for trying to game the system though, and I mean "No, we are confiscating ALL of your holdings, and sending you to prison, asshole" levels of punishment here. To have even the slightest chance of working, the penalties for gaming the system must be equivalent to ostracism from the society. (EG, the financial equivalent there to.)