Earlier quoted context omitted.
Syslog works nicely over the network in a client-server configuration, and has done so for ages.
For write-only logging from stateless, single machine bound processes - yes. For analytics, automated tracking stateful sessions across many nodes, preserving context, dumping binary fragments... no, at least for me it did not always work.
You can reconstruct almost any system flow with good logging. While that's not always ideal (especially if you need to query the data), the more structured your data gets, the less it is a simple log. When you increase the specificity of your tools, they becomes less useful in the general case, turing tarpit notwithstanding.