Honestly think its a bad idea buying such a big shiny expensive tempting present then limiting to such a minimal amount of time to actually use it. 3 hours a week is nothing, once you actually start playing an hour goes in what feels like minutes, then you wonder why they get upset at being made to turn it off and getting stroppy
DS doesn't get stroppy after an hour.
What does happen, the longer he spends on it, the more he wants to go on it and he would happily sit on it all day and night.
When he first got it, there was no limit as such. He would constantly ask to go on it, purposely misbehave on days out so he could get home to get on it, cry and throw things until he could go on it, literally sit there rocking until he could go on etc.
So I put my foot down and made it half hour and upped it to two hours a week. Now his behaviour was back to how he used to be. He doesn't live for the PS4 anymore and is back to his normal activities he enjoys.
So while you think I'm making him stroppy by not allowing him unlimited access or more access, I've actually got his behaviour sorted and I'm building up the time he has slowly and what he can handle without getting to how he was.
I also don't think screen time for hours a day is beneficial for a child. Now, he played with his other toys, he draws, he writes, he builds with Lego and his concentration and behaviour is brilliant again.