If the system is to work as designed, it's a hard question. With not-a-lot to discourage people from posting copyrighted works, there will be a lot of media on a lot of safe-harbor sites deserving of a take-down notice. Remove the first 10%, and you've not actually made it appreciably harder for those interested to find the content - you have to be at least fairly thorough. So, you are stuck filing a bunch of these notices. If you make a mistake just one time in a thousand, legitimate artists operating in good faith will be making a mistake here or there. Jailing them is not optimal. On the other hand, abuse of the system is obviously happening, and should be punished. Telling the difference, in some cases, will be difficult.
That actually doesn't matter. You're advocating someone bear the risk of a ruined life over a single mistake, and given the number of takedowns needing to be filed there will be mistakes made. Someone will have to bear the cost of that risk.
Of course, this is all leaving aside larger reforms - I just think that harsher liability is not an obvious band-aid; it has issues too.
There is however a big difference between Lawyer A: "I see I made a sincere mistake and apologize."
And Lawyer B: "Our machine gun takedown software fuzzy matches anything approaching our artist's name, or any track by him, doesn't examine the content, but just issue blanket takedowns by script."
Because the analysis is of what it does to the burden placed on artists (or those, really or purportedly, operating on their behalf) in the existing system. If the cost of a mistake is a ruined life, that side of things gets radically more expensive.
All of my analysis here is predicated on "if we want to try to make the existing system work like it is supposed to," which I will be the first to agree is not our only option; even in that restricted scope, my conclusion was "it's tough to say..."