Bonus question: How many names would one need to right down?
Real bad luck some chud hog like Light Yagami found the Death Note before anyone else did. By killing only criminals reported on in the news, he effectively made himself into a weapon of execution that could be freely wielded by the cops at almost entirely their own discretion. I wish the anime would have explored that idea a bit more, but I'll settle for the very pathetic way Light Yagami got caught by a 12 year old, threw a tantrum, and then died. That was unironically a great ending.
So say a communist found it instead. How much damage could this baby do to the global capitalist nightmare we live under?
Seriously. Reliably pulling off assassinations IRL is absurdly difficult. Even random truck or gun attacks take a lot of planning and almost inevitably result in your network being compromised and hunted down. Magic assassination book that leaves no evidence for anyone to even realize that an assassination happened? Just figure out how old the target is, pick something off the top 5 causes of death at random, and you can get rid of anybody, forever, and no one will ever know.