I've been following this question for a while now, and still - when compared to other options - would not recommend Wix... HOWEVER, that said, I came across a site the other day where the site own made mention on Facebook that 'they' had a Wix site and it was ranking well. So I went looking....
The name of their business is "Crayon Rocks", and yes, when searching for the business name you find them easily (it's the <cite class="_Rm">crayonrocks.com.au</cite> site that I'm talking about). But what about something more generic....?
So I searched 'just' Crayons. And yep, there they are - still one page 1 for my search (I'm also in Australia). Position #7.
And it's a Wix site.
Here's the thing folks; whether or not you use Wix or Wordpress or Majento or Business Catalyst - or whatever - the most important thing is your competitive keyword metrics and keyword choice, NOT the CMS of choice.
The type of content you prepare for your customers and the overall UX are far more important then H1's and H2's and whatever technical code you want to add to the conversation. Yes - the technical IS important, VERY important... but if the quality of your content in relation to the needs of your target market sucks, then it doesn't mater how damn good your site is technically, it ain't gonna help -
But... can we conclude summarily that Wix site's don't rank? No. I've seen a few now that do. But for people who don't have the money to develop a site on a (in my opinion only) a better platform, then Wix is a good starter solution.