Datadog for thousands of hosts costs tens of thousands of dollars per month. That is not a low barrier. But if you're arguing for external vendors, then Papertrail is to logs what Datadog is to metrics. And having tried both Papertrail is easier and quicker to set up (though Datadog isn't difficult).

Similarly, basic infrastructure health is not giving you the same sort of information (what the software is actually doing) that logging does. In order to do time-series monitoring of your software rather than your system, you need to spend time thinking about what metrics you need to track and how you're going to obtain them.

I run both an ELK stack and a Prometheus stack, and I find they're good for different things.