It's a good question. If you talk to the switch OS vendors like Cumulus, Big Switch and Pica8, they reliably cite financial services as early adopters, because these companies have the resources and business demands to experiment with new models that might give them an edge in rolling out new services faster.
For adoption in the general market, though,white boxes have to provide some kind of value proposition beyond being cheap, and there's still a ways to go there.
One argument might be that if you're looking to run your network like you run your server infrastructure, a Linux-based OS like Cumulus will resonate with folks who are comfortable with Chef/Puppet tools and scripting.
Then you've got the Dell strategy, where Dell provides a support and services front-end for the third-party OS. Customers still have someone to call if there's a problem, and the hardware comes from a known vendor, but they can experiment with a different switch OS.
Then there's the argument that we might want to start building networks where you swap out hardware every three or four years, just like you do with servers, because the switch silicon will continue to get both more powerful and cheaper. In this case, the white box model makes sense if you've got a network designed where you can swap boxes (and software) in and out like Lego pieces.
Of course, these are just speculations from 50,000 feet. I'd like to hear what the folks on the ground think.