Car makers are big, but to a chip maker they are a tiny customer. I suspect more than one car maker has considered making their own fab, but the costs are just too high. (My company has in fact done that, we didn't open a fab last year because of the costs - I'm not sure that was the right decision given the costs we have spent porting working software to the replacement instead, and we have a fraction of the volume of the big auto makers)
Manufacturing is a core competency of any car maker (second to supply chain). I wouldn't be surprised to see a fab partner ship between automakers in the future just to ensure they can get the chips they need. This will be at least as much about ensuring old chips don't go obsolete as about supply.
Opening own fab probably does not make sense for passenger cars. It may be reasonable for high volume long lifetime speciality vehicle producers (John Deere, etc). That will not be 'a 3nm fab', however.
Manufacturing is a core competency of any car maker (second to supply chain). I wouldn't be surprised to see a fab partner ship between automakers in the future just to ensure they can get the chips they need. This will be at least as much about ensuring old chips don't go obsolete as about supply.