Self-hosting your analytics is probably the better way to go. There's Piwik (name has changed to Matomo at some point) and I noticed Countly also has an open-source version your can host yourself. There's a lot of functionality in analytics software and you should not throw it all away and roll your own simplistic thing when you can just take a quality open-source product and host it yourself.
But I agree that applications have unique things about them and for those, people need to implement their own metrics to measure whatever interests them. In that case, the current best choices for time-series database are InfluxDB and Prometheus. They provide very simple APIs and tools for collecting and transmitting metrics, and if you prefer to store aggregations of your metrics instead of the many individual data points, you can use the very simple but powerful StatsD api/client/library/package.
Shameless plug: My company HostedMetrics (https://HostedMetrics.com) offers hosted and fully managed InfluxDB and Prometheus. It includes everything needed for a turnkey metrics platform that is ready to accept your metrics the moment you create an account: StatsD for data transmission, Grafana for dashboards, and the alerting functionalities of InfluxDB/Prometheus.
But I agree that applications have unique things about them and for those, people need to implement their own metrics to measure whatever interests them. In that case, the current best choices for time-series database are InfluxDB and Prometheus. They provide very simple APIs and tools for collecting and transmitting metrics, and if you prefer to store aggregations of your metrics instead of the many individual data points, you can use the very simple but powerful StatsD api/client/library/package.
Shameless plug: My company HostedMetrics (https://HostedMetrics.com) offers hosted and fully managed InfluxDB and Prometheus. It includes everything needed for a turnkey metrics platform that is ready to accept your metrics the moment you create an account: StatsD for data transmission, Grafana for dashboards, and the alerting functionalities of InfluxDB/Prometheus.