Tools like BareMetrics and ProfitWell do a nice job pulling revenue data via Stripe. Out of the box, tools like Mixpanel and Amplitude do a good job pulling giving you product and engagement metrics. It's up to you, though, to send all of the data over to those packages correctly and learn how to understand and interpret their reports. Other data, like burn rate, is often calculated back-of-the-napkin.
I'm working on a tool called Growth Report and shipped an MVP a little over a month ago. Hit me up if you want to check it out. aacook@aacook.co.
I suppose it could be productized, I am pretty surprised that there isn't a super-easy plug-and-play solution (a la Dropbox, Slack, etc). Probably because coming up with something that's customizable for different startups' needs must be really challenging.