I could see this actually reduce the costs in fact. Right now Tesla's all need gsm/lte support for updates. This would let the updates work anywhere in the world without the other infrastructure that's needed.

Someone still needs to invest in Starlink and pay for upkeep.

Just because you own multiple companies doesn't mean one company can provide services to the other for free.

That would be like your family member working for you and you not paying them because they're family.

This is right on. And I suspect it will also be used for Tesla to Tesla communication so Tesla vehicles share information (slow down ahead, etc) with each other.

How is it helpful for my car to send a message to space and back in order to communicate with the cars around me?

There are possibilities that can be enabled if the vehicles can communicate with each other. In the absence of other alternatives, using Starlink may be the way to do this.

Musk has specifically said that this is not a mobile solution and won't be used for his vehicles. The antennae is too large to be practical (the size of a pizza).

SpaceX won a $28.7 million fixed-price contract from the Air Force Research Laboratory for experiments in data connectivity involving ground sites, aircraft and space assets [0] so they definitely are looking to put these onto vehicles.

[0]: https://www.geekwire.com/2018/spacex-strikes-28-7m-deal-air-...

Can you quote a source for that? I did a bit of searching and can't find one. I don't see why a pizza sized antenna is much of a problem for a car.