On-premise is not old fashioned. It is indeed a requirement in several countries, for many domains including finance, banking, healthcare, telco and such. When you include PII in your analytics service, it has to be taken care of explicitly. There are indeed a few on-premise mobile / web analytics platforms for product analytics purposes that you can deploy on your own servers and retain your users' data with your own rules with no dependence on 3rd parties (disclaimer: I am cofounder of Countly).