IMHO Livermore went bankrupt to many times to be considered the greatest trader.
1. I don't know who calls that, maybe the book's title? That doesn't mean he was.
2. I think it is the lifestyle what makes you a great trader, not the number of bankruptcies or comebacks. He lived in luxury from his early 20s for 4 decades based on his trading (and not HF's fees), so in my book he was an A OK trader. Definitely in the top 10...
3. Also something to consider when we are talking about greatness, he made money in crashes when most everybody lost money. Now that is trading, baby!
4. He was called the Boy Plunger, that means 2 things: He had significant success early on to be called a boy, and having his own nickname. How many traders can you name with a positive connotation like that? (Pharma Bro doesn't apply, obviously)
-----------------------------------
Edit: You know what, I changed my mind, He WAS the greatest trader:
" When the dust had settled, between the 24th and 29th October, Wall Street had lost $30 billion. Only much later did it became known that the man who had sold short $300 million worth of shares was Jesse Livermore. Livermore had made $100 million and overnight became one of the richest men in the world.
It remains, adjusted for inflation, the most money ever made by any individual in a period of seven days. "
For weekend reading:
https://epdf.tips/jesse-livermore-worlds-greatest-stock-trader.html
Longer summary of his life:
https://www.bfsinvest.com/resources/investment-commentary/2015/3Q_2015.pdf