I wonder if we need text logs at all anymore. It seems silly to expect people to be able to read millions of log entries from tens, hundreds or even thousands of servers. Maybe binary logs using protocol buffers or thrift are the way of the future.
Protobuffers or Thrift can definitely be smaller in byte size, which does matter somewhat, but JSON right now is just more easily accessible.
I think in a few years, assuming JSON logging really takes off, you'll see people using these other RPC formats in order to optimize and reduce the size of their messages.
I view 'better' RPC formats as a performance optimization of the same basic idea though: Easily add new fields, and use a format designed for computers to consume.