Well... the only flaw with this plan, is that I fear the VAST-VAST-MAJORITY of winners would not be capable of investing wisely at 7% per year.
You might be able to do so. But I would venture to guess that most people can not. It's not as easy as it seems for most.
Thus, I would argue strongly that for MOST people, the best option is indeed to take the yearly or monthly annuity instead.
But nevertheless, assuming a genuinely wise financial investor, then yes, I do agree with the basic premise of your argument.
Like you, I would actually be capable of earning more money in the long run, by taking the lump sum instead.
So just like you, I too would take the lump sum as you have suggested.
I would leverage the benefits of the lump sum, by investing in a relatively low risk way, with a SOLID basket of high dividend paying companies (that are WELL MANAGED, and have a history of steady/constant dividend increases over multiple decades).
Of course each company I add to my basked, would need to have LOW debt, and be a strong leader in their sector, and ideally they would not need to "innovate" in order to maintain their cash flow.
HOWEVER, by utilizing a conservative, low risk, dividend style of investing, within the first decade, you would probably be lucky to get only about 3 to 5 percent per year in dividends, for your shares in those companies.
BUT... in subsequent decades, that would very likely increase to 7 to 10 percent per year (since these companies are reliably and constantly increasing dividends year after year).
So each year you get a dividend "raise" in your income (most years at least).
In subsequent decades, you would then likely be earning 10 to 15 percent on your dividends... and that would only continue to go up in time.
Also, if you buy extra shares during market crashes, then you can really boost your dividend income VERY NICELY!
As well, as an added side bonus, your actual shares will undergo a slow/steady capital appreciation, likely doubling your initial investment value within about 1 to 3 decades.
For a good introduction to dividend investing in this way, I would recommend the series of books by the investor Derek Foster.
It is claimed, that he was able to essentially retire in his mid 30's by pouring all his money into great dividend paying companies.
No investor is without controversy, or follows their own method perfectly without error... but you will indeed learn a lot from his books, if this type of investing appeals to you.
Essentially, it's always nice for corporations to PAY YOU for a change, in the form of regular monthly or quarterly dividends!