We recently fixed a bug with incomplete requests by noticing in nginx logs that the size of the headers + the size of the body was the size of the buffer of a linux socket.
It's not uncommon to see companies talk about processing terabytes or even petabytes of log data per day. In the end the storage isn't that expensive [1], and you can discard everything after a little while.
[1] Assuming of course that any company generating a petabyte of logs every day is doing so because they have an enormous number of customers, AFAIK the cost of storing 1PB of logs on something like Glacier is in the 100-300k USD/yr range. Absolutely a tolerable expense for the peace of mind you get by knowing you can go back in 2 months and find every single request that touched a security vulnerability or hunt down the path an attacker took to breach your infrastructure.
No, not affiliated with datadog, and not convinced the cost/benefit ratio is positive for us in the long run.