Don't set it up as forbidden fruit. The minute that happens, it becomes a power struggle that is no longer about the desire to have more screen time but a desire to push the boundaries.
I never limited screen time for my kids, and the older two are in college pursuing degrees, so I don't believe it killed their brain cells or turned them into mindless lazes.
What I did do was make sure there were enough other activities that their interest were expanded beyond the screen and that the time was limited by default because we were doing other things, Screen time became a way to unwind, get away from the stimulus of other people or to pursue in depth individual passions and interests. We went to the park regularly, made three times a week trips to the library, visited the children's museum, went shopping for groceries, etc. I had a stool in the kitchen so the kids could come and "help" with cooking - even if it was just sticking their fingers in things to taste them. The kids had a little table near the kitchen with craft things that changed to adjust to their ages. And when they got so immersed in a new computer game that I thought their brains and eyes needed a break, I simply announced that it was enough time on the computer so it was time to do something else. And if the protested and gave me attitude, I unplugged the computer and told them that their attitude had ruined their opportunity to play any more that day. They became quite willing to log out of a game and go do something else, because they knew there was no room to whine their way to more time.
I also never separated fun vs. educational or skill building. Kids innately like to learn, and our kids like to learn intensely. I wasn't preparing them to be prodigies - so I let them drive the learning process. That being said, I did limit what I found to be awful programming. When they're four, you can still do that,
I seriously wouldn't make this a battle or a hill to die on. There will be other power struggles that you MUST win, so I wouldn't pick ones that can be addressed without setting it up to be a power struggle.
