However, a Chrome-with-Google-revenue would be far more independent of Google than Chrome-the-Google-Subsidiary. Mozilla/Firefox has shown that it's still possible to advance privacy even within such an arrangement.
Also, its far from clear who would have the most power in such an arrangement. Without a popular browser of its own, Google will be forced to pay the browser vendors to stay the default, unless it wants to give a search engine competitor a chance to unseat it.