Do you mind expanding on that?

With APIG+Lambda you get CloudWatch integration 'out-of-the-box', and can expand the metrics and logs you send out with a few added lines of config.

You can also toggle X-Ray for a detailed view of your call graph.

If the default implementation isn't good enough, you can define your own CW events, alarms, and log filtering.

I'll grant you that you can't just ssh into a host and tail some logs, but if you're keen you can send your logs to elasticsearch for a better arbitrary search experience.