Brand bidding is always a controversial subject. I certainly know of companies who would happily explore solutions to make it go away.
Google+ with the integration into Search+ may now be such a solution.
Google is testing adding "latest posts" into the right-hand side of the search results. This does not get rid of all the PPC because ads can appear at the very top or the very bottom. It's just harder work to qualify for the top position and not as an effective brand bid to be in the bottom.
The screen grab below shows the effect in place for my name. I'm no brand. I've a fairly small social media footprint - so if my name can trigger this response then this level of SERP dominance is certainly within reach for most brands. If, that is, Google decides to roll it out and if we ever see Search+ outside of America.
I hope we do. I like Search+.