I’m in agreement with most of this. Wise, prudent lottery players do exist in significant numbers, contrary to the blow-it-on-a-spree-and-scammers stereotype.
In Canada there are two large national lotteries; Lotto 649 and Lotto Max. 649 is played twice a week, Lotto Max every Friday. Both hand out a very large sum of money, anywhere from $5 million to $60 million depending on how long the jackpot builds. I don’t know offhand how often it goes un-won or how often it gets split - I could figure it out but it would take a long time - but between the jackpots and Lotto Max’s secondary prizes of $1 million (note; Canadian lottery wins are paid in full, up front, and there is no tax on them, so you actually win the advertised amount) I’d say at least 100 people a year are made millionaires.
If they all blew out of cash in no time I would think this amazing plague would be a news item of sorts. Some journalist would be pursuing that story; the winners’ names are public knowledge, after all. But no one has, and the claim ALWAYS goes back to the near-apocryphal 70% statistic.
If you win a really, really immense amount of money, like if you won the $50 million cap on the Lotto Max, or won a record setting Powerball, it would not be quite as easy as you believe. The part where you stash the money and live off the huge interest payouts, that part is easy; $50 million at a measly 3 percent is a staggering $125,000 a month, taxed as a capital gain. Financially you have nothing to worry about ever again and you would have to be a colossal idiot to blow it.
But you are going to be harassed. Every charity in town - every one - will target you to beg for donations. And hey, why not? The women’s shelter needs money and of course they’re going to ask you, you’ve got a lot of easy money; they have bills to pay on a shoestring budget and will get the money wherever they can. Every con artist for a hundred miles around will have you on their list, and why not? They’re con artists and people flush with money are easier marks. Every relative you forgot you had, every friend who just needs $40,000 to get that restaurant started up, people you never heard of, are going to come around with their hand out. I assume you have family; believe me, there will be hard feelings that you in no way are at fault for creating.
If you want to carry on with your life you’ll have to take a few prudent steps to dial down the heat.
Another reason why you really don’t want a tiny chance at 50 million+ but rather a much larger chance of something like 1 - 3 million, which will let you fly under the radar to a much larger degree.
For middle class and more wealthy people, it’s probably not a big deal- about all you’re doing is enabling them to have or do nicer stuff than otherwise.
But in large part, the people with the attitude you described earlier aren’t liable to be even middle-class wealthy, and their heirs could probably do with a leg up from the previous generation.
It’s more looking at the family as the unit that retains wealth rather than it being a strictly individual thing.
At my age $50 million is way too much for me. $1 million I can live with comfortably. I don’t have any friends so that’s no problem.
I can tell everyone to GTH and sleep well at night.
Just calmly, firmly, say no. Frankly, I would take pleasure in saying no to people who shouldn’t get donations from me. I could carry out printed news articles with me about lottery winners who went broke from giving to everyone. When someone comes to me asking for money, I would just hand them the printed articles, “This is precisely why lottery winners go broke. Are you trying to get me to go broke, too?”
Armor up your house to be a fortress. Have doors with an interface for video/audio communication (where you can see and hear people outside but they can’t see or hear you) so that you can talk to people without opening your door for them.
I like the idea of the person who told everyone, “Just talk to my financial advisor, he handles my finances.”
I’d just say, “I gave at the office.” 
You’re talking to the world class asshole that once gave a street beggar an empty beer bottle. I think giving every single outstretched hand something would be fine - Here’s a dollar, go buy a lottery ticket.