That said, I scare-quote "screen time" because I believe it promotes weak thinking about the problem. The problem, in my somewhat considered opinion, is not simply the screen. My concerns have been more about effort expended and the real vs. perceived (by the brain) results that are received. Video games, movies, and a lot of apps (even putatively educational ones!) have the problem that you exert little to no effort and you get these superficially amazing results. You click a few buttons and holy cow, you're playing Beethoven's Fifth Symphony! My objection to this is that it trains your brain at a very deep level, very early, to the idea that such results come from very little expended effort of any kind, not cognitive, not physical, not any effort. This is basically a lie. That is not how the world works. In the real world, you need to work. (Put aside the details of how much for a moment; there is no forseeable future in which life is as easy as these "screens" present.)
I think "addiction" is not the core problem, but a secondary effect of the above; you get addicted to the "screen time" because your brain very rationally decides that the best way to get rewarded in a given period of time is to put its effort into the "screen". And it's really hard to override the lower parts of your brain when they make what is, from their perspective, such a rational decision. I'm not even convinced it's a good idea in general.
(As the conscious "part" of me, I find there's much more mileage in learning how my foundational brain systems are making their decisions, and arranging it so that they receive the input that will produce the output I want, rather than berating them for producing the wrong output.)
My oldest is now 9. At that age, yes, I did get a lot of "screen time", but it wasn't on the internet, and playing games on the Commodore 64 has its own lessons to teach about patience, and even if it did reward my brain, it couldn't keep up with modern video games and often lost out even to just reading a book, so it's not like it is today. So I have, without shame, limited my children's "screen time" even beyond what limits I had as a kid, because of those differences. Also they have zero access to the internet, again without shame. (There's plenty of adults who frankly can't handle the modern Internet, to be honest.)
Now, I'm still in the early days of this, but recently my oldest has been getting into Scratch. I picked up the Humble Bundle Makerspace bundle [1] (4 more days!) and he's been working his way through the "Super Scratch Programming Adventure" at a decent pace, without much prodding from me. And now the payload of what I'm setting up here: When he's doing that, as long as he's making reasonable effort and progress (as opposed to just screwing around endlessly in the paint editor; there is a difference between exploring and trying to make pictures and trying out the tools, and just aimlessly scribbling, etc.), I don't count it as "screen time", because I don't think it has the characteristics of "screen time" that harm children.
Our kids are 9 and 7 right now, and the message I've been giving them lately is "I want you to have something you're doing, unrelated to school. It can be soccer. It can be piano. It can be learning about programming or learning to draw or anything else. You don't have to stick with it forever, in fact I want you to try lots of things out over time, but you have to be doing something not related to school." Early results are promising. This week they're learning about the pets they are about to get from library books.
Of course other parents with other kids may have other problems; perhaps your kid needs to be encourage to stick with things a little longer, perhaps you need to remind your kid after 3 years of the same thing that they should probably spread their wings a bit. But that's my experiences, I don't have any others. :)
I do plan on loosening up over time. I do expect that there will be troubles in the future with too much access. I'm hoping the foundation I'm laying now will help me point out to them the consequences of what is happening. Ask me again in 10 years. I'm sure it won't go swimmingly, but who knows how it will actually go.
[1]: https://www.humblebundle.com/books/makerspace-books?hmb_sour...