I don't see it as luddite at all any more than not allowing your kids to use cocaine means you are against pharmaceuticals or medicines.
The problem isn't the screen. It's what's on the screen. It's specific products that are engineered to maximize addiction.
Our kids play video games and we don't limit access to kids Netflix and many other things. They'll play games, watch a show, whatever, and then do something else. With YouTube they would watch, and watch, and watch, and watch, forever, to the exclusion of all other activities, and when we looked at what they were watching it was 100% repetitive content-free mesmerizing trash.
The biggest difference we saw is that when friends were around they'd drop video games or shows to play with their friends, but with YouTube they would not. Nothing could compete with trash YouTube videos. Examples included random incoherent blabbering while playing video games, videos of cars running over expensive things, unboxing videos, disturbing AI-generated trash, etc. The algorithm seems to have a bias toward increasingly mindless content. You can start with something mildly interesting and pretty soon you're watching someone smash things for six hours.
I see a few replies here questioning this and being like "but my kids are fine." It's possible that different people vary in terms of their susceptibility to this stuff in the same way that different people vary in, say, their propensity to become addicted to opioids. There are people who can use opioids for a while and then just walk away and there are people who use them once and think about them for the rest of their lives. The difference is probably genetic or brain developmental.