I would be interested in seeing how you define non-privacy invading uses. I ask this because I suspect that there may be a fundamentally different set of assumptions in play among different parties to this discussion. Making those assumptions explicit may help us make progress. That trouble mirrors, however, the difficulty a user would have in understanding the relationship between the sites. The domain remains ubiquitous and easily verified.
Measurement is important.
You may have to go beyond your current implementation to make this work, but I believe it is possible to continue to use advertising networks under the current spec. It is simply difficult to do so without the user knowing that the advertising network has become involved. That is the intention of the current design. The deployment of such a mechanism presents problems far beyond those of the current spec. It also completely ignores the problem of legacy browsers without this capability.