You're forgetting localization. Your timezone alone makes you more identifiable. Add in your IP address and you're pretty identifiable. Not to mention that iPads don't really have any private browsing mode.
> Not to mention that iPads don't really have any private browsing mode.
Safari on iOS certainly does have "private browsing". Just go to the Settings app and select "Safari" from the top level and it's the first setting under the "Privacy" (just below the "General" section). When it's enabled, the browser looks different to let you know -- the normally gray bezel UI becomes black. This has been a feature ever since iOS 5.0 was released in 2011.
I just tried Panopticlick both before and after enabling private browsing in Safari (Mac OS X) and the site identified the same number of identifiable pieces of information about me. So it looks like that has no effect.
Which sort of makes sense - the info it's looking at is basically the header info. Screen size, installed fonts, IP address, and so on. It's not relying on cookies, as cookies can't be seen/read across domains (you can't tell I'm an Amazon customer if I just visit you out of the blue).
CSS may color visited links red, but they hacked getComputedStyle to return the normal color instead. So, you can't tell if that link to Amazon you just created is visited or not.
And you can no longer set, for example, font-weight:bold for visited links, because that would change the size of the element, and they decided, unlike in the color case, that it would be too complicated to get all the APIs to lie about the new geometry.
True, timezone could be a biggie. Although in my case (GMT) is 1/22. Screen res is another possibility (1920x1080) = 1/28.
All the site doesn't mention anything about IP address on the report page and presumably doesn't have access to third party tracking cookies however so private browsing shouldn't make much difference (I cleared my cookies and got the same score).
iOS Chrome has "Incognito Mode*". The asterisk is there because WebKit does not have any way to make localStorage private, meaning it's shared between Incognito and Normal browsing modes, so there's a possible leak of information there, especially if they're using a third party tracking service. This is true for any of the private web surfing apps that use WebKit.
It only clears your browsing traces locally (history, cookies, cache, etc). Everything else can still be tracked on server-side. BTW, every private browsing mode that I know works pretty much that way.
In the current model real privacy can only be achieved running something like Tor.
