I think this is mostly a myth when it comes to consumer software. People say they like privacy/confidentiality/security but they are not willing to make any compromises to get it even if those compromises are very small in comparison to the privacy/security wins.
I do know a a few data points: (EDIT: walterbell provides a very good data point below, and one that should have been obvious to me!)
* Some vendors of confidentiality services report increased demand, especially since the Snowden revelations. (Sorry, I don't remember who reported it.)
* Facebook and others now are emphasizing privacy, suggesting that they see demand for it.
* A recent consumer survey said confidentiality concerns were impacting purchases on mobile devices.
* Also I read in an advertising industry publication that when a retail store chain posted signs saying they were tracking customer activities (via wifi/bluetooth on mobile devices), they got many complaints and saw an impact.
* Their solution of course was to take down the signs, which raises another point: If consumers/citizens don't care about surveillance, then why are businesses and government secretive about it?
I know almost nothing about marketing consumer software, but if Mozilla/Firefox established itself now as the leaders in privacy, they may have an insurmountable lead in consumers' minds when/if the market moves that way.
(I realize the same could be said about any product/feature for which there currently is little demand: 'If Mozilla/Firefox started providing free cheezy-poofs with their browser now, they'd have an insurmountable lead when the market moved that way.')
That's a design & engineering problem which can solved for specific use cases. Snapchat's user base & 10 billion dollar valuation is one example.
It creates the illusion of it but its illusion is extraordinarily thin.
Please don't perpetuate the myth they are private or secure.
http://www.informationweek.com/software/social/5-ways-snapch...
http://www.nbcnews.com/tech/security/oh-snap-snapchat-fixes-...
http://gibsonsec.org/snapchat/fulldisclosure/
http://money.cnn.com/2012/12/28/technology/security/snapchat...
etc.
User perception of relative privacy has lead Snapchat to the point of having a large user base and significant funding, i.e. it demonstrates user demand for privacy. The quality of Snapchat's product is another matter, but they now have the resources to be private and secure, if they so choose.
TextSecure is doing good work in private messaging, hopefully their iOS version will raise the bar for everyone.
However, when all it takes is someone deciding they want to copy the picture and spread it...I think it results in a dangerous situation where the "customer" thinks its secure/safe but the reality is it isn't. I've seen so much damage caused by that sort of event that I take the idea that people consider such things "secure" or "private" offensive.
The security community is culpable for failing to find meaningful middle grounds that are acceptable to customers and which generate the revenue that can fund the development of strong security. As a result, non-infosec people build "good enough for naive users", get traction and fix only when forced by a breach or failure.
There are two ways to find (in the Steve Blank customer discovery / product management sense) a profitable middle ground: (1) start out with a weak security posture until public breaches force improvements to a stronger "good enough" (2) start out with strong architecture and consciously weaken to find a "good enough" point that is usable by a mass audience.
What alternative do Snapchat customers have today? TextSecure is subsidized by Twitter, let's hope Twitter has a long future. VC-backed Wickr is going after the financial sector. We need more security people who are not offended by scenario #2, because their distaste for the option makes them most qualified to make difficult compromises and disclose the associated risks so that customers can make informed choices.