From initial discussion with Mike, there are two parts that would be needed for a (self hosted) setup:
a) The hosting itself (this is something I can likely help with)
b) Setup and ongoing management of Piwik. This isn't a skill set I have (nor am interested in). However I'm generally thinking the Homebrew Community is big enough to rustle up at least a few people with the right skill set for getting this done (and keeping it done :>).
Trying to get both hosting + Piwik setup/mgmt from the same set of people may be a tall order, so doing them separately is probably more achievable.
As a data point, this kind of approach - sponsored hosting/hw/similar + volunteers to look after Community infra - is used successfully in other projects. PostgreSQL is a good example.
Can't really think of any obvious reasons it wouldn't work for Homebrew too. ;)
Additionally, this (kind) offer is pointing to other organisations that may be able to host the servers and discussing potential solutions to the other options. It's not a slam-dunk by any means.
This is all done in my free time so I don't need an excuse to do or not do any of this.