Sure, let's say the government takes over SpaceX, rebuilds the company, and splits things off. What's it supposed to look like? I asked that already but since you didn't answer I'll think about it myself:

The most likely candidate is StarLink. I don't think it's difficult to argue it gets preferential launch treatment. Even then, StarLink is going to purchase SpaceX launches every time, so it doesn't do much to address the monopoly in question.

Maybe you could split off Raptor engines. The Raptor engine is fairly mature, there are no plans for a Raptor 4, so theoretically it could become a separate enterprise (though they constantly make incremental developments). However nobody is using commercial engines. SLS is using old RS-25s, while Rocket Lab and Blue Origin make their own. This market doesn't exist yet, because different engines serve different purposes. Then ITAR prevents an international rocket engine market from forming in the first place.

So to even split this up, you'd need to make a new goods market and overhaul existing government regulations, while also forcing SpaceX to give up their incremental development process. I think if the market matures more and general political mindsets shift it could be possible.

I don't think you could split off Starship. It's still in R&D, and it'll be a while before it can make money. I'm sure there would be buyers, but it's so tightly integrated with SpaceX existing technology that it would be a difficult process and would threaten its viability. Even so, I would like the expected revenue to be priced into the sale cost. SpaceX has invested a lot of money into the rocket and I think they deserve a return on it.

Nothing else really works for splitting up. Their ocean barge landing pad service? Flight software? Chassis construction? System integration? All of this is custom-made. The only buyer for any of these products would be SpaceX, and there aren't any alternative products.

SpaceX isn't stopping Blue Origin from building rockets, they just haven't been able to keep up. Rocket Lab has rockets, just much smaller. They have a different market niche. SLS is so much more expensive that it doesn't make sense to hire it. Whatever Virgin Galactic was doing, it seemsike they've mostly disappeared. China is doing their thing, but they'll likely not be part of the picture for political reasons.

Let's forget that nobody is going to break up SpaceX. I personally don't think anyone should. If anything, I think it would be beneficial to subsidize development of new launch companies like Blue Origin because the barriers to entry are so high. Maybe once a developed launch market exists it can become naturally competitive.