As long as they exclude publically traded companies where there isn't a single controlling party this sounds like a good idea. Scary for those that like to ignore laws, but good for everyone else.
There's extensive case law in the EU about this. The interesting part in the case of Musk's companies is that they would be pretty much shielded from X's fines if he hadn't used Space X's and Tesla's resources and personnel while trying to fix things on X/Twitter.
This is why it makes sense for specifically private companies that are solo owned. It's not uncommon that resources get shifted from one to the other as they are often treated as personal not corporate assets.
USA has been stepping up their enforcement the last few years, but they got their hands tied after Supreme Court overturned Chevron. So you're probably right.