If only that were true... I have some experience in this area through my previous employer (Qualcomm/Globalstar) and there are significant regulatory hurdles to get this kind of network operational in a surprising number of countries. Basically they want the traffic to go through their own ground station where they can legally control it or illegally intercept it. The various newcomers (OneWeb, SpaceX's satellites, Intelsat's new constellation, Iridium Next) expect to be available and profitable in enough places to put pressure on the others to also open up, but that's a long term plan. It won't "work everywhere" on day one.and the advantage is getting bigger as Elon launches more satellites for networking. GM and I'm sure others can negotiate deals with cell carriers to add data connectivity to their cars, but will have to do this per region/country, Tesla's network will work everywhere
(You know that Iridium got its name from the number of satellites in the original plan... for some unknown reason they wouldn't change the name to Dysprosium when it downsized though. )