As I said, responding to another comment of yours, a distributed system I worked on produced a few GB a day. The logs were rotated daily. They were never transmitted anywhere, during normal operation. When things go wrong, sure, we look at them, and generate even more logging. But that was rare. I cannot stress enough how much of a non-issue log volume was in practice.
So I ask you to quantify: What counts (to you) as voluminous, as in daily log file sizes, and how many times they are sent over the network?