We've had trouble with a few very specific activities re: screen time. Mostly, we've not seen a reason to limit screen time as a whole-- DD would far rather read than watch.
The exceptions were very specifically role-play related, and 'virtual reality' with a social twist. Webkins was the first of those things. (ugh. Like crack for kids.)
That taught me a lesson-- I've said NO to Minecraft, and I keep her passwords for some other similar activities like Roblox. When she starts one of those activities, we give her a finite time limit, and if she balks when it's up, she knows that we'll deduct time the NEXT time.
Skype has also been problematic at times.
In general terms, though, DD has gone through periods where her screen time was pretty high. Definitely higher than official recommendations, and way higher than we'd likely admit to our social circle. But I firmly believe that HG+ kids are simply.... different... when it comes to screen time. It's that fire-hose mentality at work.
I also agree about not allowing it to become a power struggle. We found that the single best way to limit this was to have a crappy cable package. Heheh. She doesn't watch much television when there isn't anything 'good' to be had there. I suspect that dial-up would have cured the Webkins problem, too, but the adults in the household needed the high-speed. Darn.