Carplay can work wirelessly if the infotainment system is able to work that way. It's not a limitation on Apple's side with any recent-ish phone (this decade, at least, and I think late last decade). This is on the manufacturers.

As far as I know in some cars you don't need a cable.

It doesn't need a cable. Even the base model Hyundais support Wireless CarPlay now.

You can get a wireless CarPlay adapter for cheap and just leave that plugged in.

And that page 18 seems to have nothing to do with the car manufacturer.

My car has wireless CarPlay and I use it daily. There is one quirk I have noticed and I’m not sure if it is a general issue with wireless CarPlay or just Volkswagen’s implementation and that is there are times that the phone gets disconnected and the infotainment screen goes black. My assumption is that it has to do with a signal that is stronger disrupting the connection causing the issue as it only happens in certain areas and not always. The latest area I know it will happen is on a bridge that is having construction done on it. When we get over the construction equipment the CarPlay disconnects and will reconnect a few minutes down the road. I’ve actually wanted to get a HackRF One to capture the signal and see if I could tell what it was but I can’t justify spending $300 for just that.