You people that say you wouldn't want to win baffle me. Just don't tell anyone but a tax lawyer from a top 10 US law firm, have him/her set up trust (blind perhaps) and give the lottery ticket to the trust. Now you are the billionaire next door that nobody realizes.
While I would want to win, it often isn't as simple as this and often you are required to not be anonymous. I don't know if there is truly no way around that, but it may not be possible to just not tell anyone.
I'm sure there would be greedy people coming out of the woodwork, and that would be unpleasant. With the insane sums of this particularly jackpot, you can throw a lot of money at that problem, however, which would mitigate it, it not stop it entirely. Establish a non-profit trust of some sort, hire someone you trust thoroughly, and tell anyone who asks that all requests for money need to be directed to that entity. Repeat as often as necessary.
Sure, there are downsides. And yes, I think we are all more or less equipped to deal with the kinds of problems we grew up around, as sort of a cultural literacy. When our situations change dramatically, we are suddenly faced with a set of problems for which we don't have that same literacy. I imagine it's a bit like moving to another country and not knowing simple things. But I can't imagine the upside, for me, wouldn't outweigh the downside. I'm not as minimalist as many here, and 2000 sqft within walking distance of the beach, and month in Europe every year, while neither DH nor I ever had to go to work, would be incredible. I suspect we'd still play at finances since we find it interesting. If you have half a billion dollars, you probably don't need rental properties, but I'd still make it a hobby. And maybe, if the right person came along, my "giving" branch could have one of them to provide free or very low cost rent to someone deserving. Being able to do that on a large scale would be incredible.