Well, GA is quite convenient - we get pretty graphs, realtime analytics and so on. It's not something we have considered moving away from, since it's trivial to disable it entirely. And it's not significantly worse than any other tracking tool.
I'd say it's substantially different from hosting your own Piwik, OWA, or even something like snowplow - where you could elect to avoid IP storage.
That said, those all entail a lot of work and/or additional cost. You're also absolutely right that allowing users to disable it (and ads) is an amazing feature.
Piwik is really ancillary to the discussion at hand, but I often see the claim that Piwik can't handle busy sites, and it's important to quantify the claim.
I've had success (and others report similar behavior) with 500,000+ hits per day. http://piwik.org/docs/optimize/ reports adequate support to higher levels. It's quite easy to set this up with EC2 + RDS, and using autoscaling gets you a very resilient solution that can easy handle those numbers. Also, in the case of mediacru.sh, many of the optimizations have little impact since they optimize for reporting on the already-gathered analytics. With only two analytics viewers/users - this is not much of an issue.
If you're doing more than 1mil per day, then I think something like snowplow, a commercial solution, or a fully custom solution are appropriate anyway.
Well, GA is quite convenient - we get pretty graphs, realtime analytics and so on. It's not something we have considered moving away from, since it's trivial to disable it entirely. And it's not significantly worse than any other tracking tool.