All of that still happens even with the FDA approving drugs. Luckily we have class action process
Class action is what I meant with the difficulty of organizing. To make a class action happen and win, the damage done must be massive enough to get enough people to notice it and take action, and must be easily and cheaply provable. A class action is not going to fund expensive scientific studies that prove their problem was caused by the company they're suing. Your solution would only prevent the absolute worst cases. Any damage that's rare, hard to notice or prove, small, long term, etc would not get compensated and would cost society much more than properly funding FDA.