Except for the part where anyone you'd like to partner with isn't going to trust your internal analytics to gauge your popularity. One of the points of third party analytics is that you have a disinterested third party who can provide the data to someone else.

If I use self hosted analytics and exception tracking I have to ensure its up-to-date with security patches. The pros will do a better job at this than anyone will self hosting. Concentrate on your core business, knowing when to outsource is important.

As someone running an ecommerce website without using advertising conversion tracking from to our various advertising networks it would simply not be measurable or cost effective. It is an essential part of how the systems works.