I did this after I learned that Safari on iOS does this by default. If in all of my usage of my phone browser I didn't run into issues, I don't see why I should on the desktop.
How so? You can't really get around not using third party cookies by doing something different, and if you can, are you really going to detect the device type rather than whether the UA accepted third party cookies? I guess anything is possible. All I know is that turning off third party cookies has not affected me in any way over the past three months. Then again, I block advertisers at DNS and via ABP, and they are the main user of third party cookies, so I guess you could say that the ads didn't properly work for me for a while.
